Status

Current state: <TODO>

Discussion thread: <TODO>

JIRA: <TODO>

This method is easier to use, but it also limit some possible optimizations

Released: <Flink Version>

Please keep the discussion on the mailing list rather than commenting on the wiki (wiki discussions get unwieldy fast).

Motivation

Iteration is a basic building block for a ML library. It is required for training ML models for both offline and online Training. In general, two types of iterations is required:

1. Bounded Iteration: Usually used in the offline case. In this case the algorithm usually train on a bounded dataset, it updates the parameters for multiple rounds until convergence.
2. Unbounded Iteration: Usually used in the online case, in this case the algorithm usually train on an unbounded dataset. It accumulates a mini-batch of data and then do one update to the parameters. 

Previously Flink supported bounded iteration with DataSet API and supported the unbounded iteration with DataStream API. However, since Flink aims to deprecate the DataSet API and the iteration in the DataStream API is rather incomplete, thus we would require to re-implement a new iteration library in the Flink-ml repository to support the algorithms. 

And there is another performance issue with the DataSet::iterate(...) API: in order to replay the user-provided data streams multiple times, it requires the runtime to always dump the user-provided data streams to disk. This introduces storage and disk I/O overhead even if user's algorithm may prefer to cache those values in-memory and in possibly a more compact format.

In order to address all the issues described above, and make Flink ML available for more iteration use-case in the long run, this FLIP proposes to add a couple APIs in the flink-ml repository to achieve the following goals:

• Provide solution for all the iteration use-cases (see the use-case section below for more detail) supported by the existing APIs, without having the issues described above.
• Provide solution for a few use-cases (e.g. bounded streams + async mode + per-round variable update) not supported by the existing APIs.
• Decouple the iteration-related APIs from core Flink core runtime (by moving them to the flink-ml repo) so that we can keep the Flink core runtime as simple and maintainable as possible.
• Provide iteration API that does not enforce the disk I/O overhead described above, so that users can optimize an iterative algorithm for best possible performance.

Target Use-cases

In general a ML algorithm would update the model according to the data in iteration until the model is converged. The target algorithms could be classified w.r.t. three properties: boundedness of input datasets, amount of data relied for each variable update and the synchronization policy. 

1) Algorithms have different needs for whether the input data streams should be bounded or unbounded. We classify those algorithms into online algorithm and offline algorithms as below.

• For online training algorithms, the training samples will be unbounded streams of data. The corresponding iteration body should ingest these unbounded streams of data, read each value in each stream once, and update machine learning model repeatedly in near real-time. The iteration will never terminate in this case. The algorithm should be executed as a streaming job.

• For offline training algorithms, the training samples will be bounded streams of data. The corresponding iteration body should read these bounded data streams for arbitrary number of rounds and update machine learning model repeatedly until a termination criteria is met (e.g. a given number of rounds is reached or the model has converged). The algorithm should be executed as a batch job.

2) An algorithm may have additional requirements in how much data should be consumed each time before a subtask can update variables. There are two categories of choices here:

• Per-batch variable update: The algorithm wants to update variables every time an arbitrary subset of the user-provided data streams (either bounded or unbounded) is processed.

• Per-round variable update: The algorithm wants to update variables every time all data of the user-provided bounded data streams is processed.

In the machine learning domain, some algorithms allow users to configure a batch size and the model will be updated every time each subtask processes a batch of data. Those algorithms fits into the first category. And such an algorithm can be either online or offline.

Other algorithms only update variables every time the entire data is consumed for one round. Those algorithms fit into the second category. And such an algorithm must be offline because, by this definition, the user-provided dataset must be bounded.

3) Algorithms (either online or offline) have different needs of how their parallel subtasks.

• In the sync mode, parallel subtasks, which execute the iteration body, update the model variables in a coordinated manner. There exists global epoch epochs, such that all subtasks fetch the shared model variable values at the beginning of an epoch, calculate model variable updates based on the fetched variable values, and updates the model variable values at the end of this epoch. In other words, al subtasks read and update model variables in global lock steps.

• In the async mode, each parallel subtask, which execute the iteration body, could read/update the shared model variables without waiting for variable updates from other subtask. For example, a subtask could have updated model variables 10 times when another subtask has updated model variables only 3 times.

The sync mode is useful when an algorithm should be executed in a deterministic way to achieve best possible accuracy, and the straggler issue (i.e. there is subtask which is considerably slower than others) does not cause slow down the algorithm execution too much. In comparison, the async mode is useful for algorithms which want to be parallelized and executed across many subtasks as fast as possible, without worrying about performance issue caused by stragglers, at the possible cost of reduced accuracy.

Based on the above dimensions, the algorithms could be classified into the following types:

*Although SGD-based algorithms are also batch-based, they could be implemented with an Epoch-based method if intermediate state is allowed: the subtasks could sample a batch from all the records from the position of the last batch. 

Based on the above classification and the replacement implementation for SGD-based algorithms with bounded dataset, we mainly need to support

1. The synchronous / asynchronous epoch-based algorithms on the bounded dataset.
2. The synchronous / asynchronous batch-based algorithms on the unbounded dataset. 

Overview of the Iteration Paradigm

Based on the types of algorithms, we explain the iteration paradigm that has motivated our choices of the proposed APIs.

An iterative algorithm has the following behavior pattern:

• The iterative algorithm has an iteration body that is repeatedly invoked until some termination criteria is reached (e.g. after a user-specified number of epochs has been reached). An iteration body is a subgraph of operators that implements the computation logic of e.g. an iterative machine learning algorithm, whose outputs might be be fed back as the inputs of this subgraph. 
• In each invocation, the iteration body updates the model parameters based on the user-provided data as well as the most recent model parameters.
• The iterative algorithm takes as inputs the user-provided data and the initial model parameters.
• The iterative algorithm could output arbitrary user-defined information, such as the loss after each epoch, or the final model parameters. 

Therefore, the behavior of an iterative algorithm could be characterized with the following iteration paradigm (w.r.t. Flink concepts):

• An iteration-body is a Flink subgraph with the following inputs and outputs:
  • Inputs: model-variables (as a list of data streams) and user-provided-data (as another list of data streams)
  • Outputs: feedback-model-variables (as a list of data streams) and user-observed-outputs (as a list of data streams)
• A termination-condition that specifies when the iterative execution of the iteration body should terminate.
• In order to execute an iteration body, a user needs to execute an iteration body the following inputs, and gets the following outputs.
  • Inputs: initial-model-variables (as a list of bounded data streams) and user-provided-data (as a list of data streams)
  • Outputs: the user-observed-output emitted by the iteration body.

It is important to note that the users typically should not invoke the IterationBody::process directly because the model-variables expected by the iteration body is not the same as the initial-model-variables provided by the user. Instead, model-variables are computed as the union of the feedback-model-variables (emitted by the iteration body) and the initial-model-variables (provided by the caller of the iteration body). To relieve user from creating this union operator, we have added utility class (see IterationUtils) to run an iteration-body with the user-provided inputs.

The figure below summarizes the iteration paradigm described above. The streams in the red color are inputs provided by the user to the iteration body, as well as outputs emitted by the iteration body to the user.

Public Interfaces

We propose to make the following API changes to support the iteration paradigm described above.

1) Add the IterationBody interface.

This interface corresponds to the iteration-body with the inputs and outputs described in the iteration paradigm. This interface should be implemented by the developer of the algorithm.

Note that the IterationBody also outputs the termination criteria which corresponds to the termination-condition described in the iteration paradigm. This allows the algorithm developer to use a stream created inside the IterationBody as the terminationCriteria.

package org.apache.flink.ml.iteration;

@PublicEvolving
public interface IterationBody {
    /**
     * This method creates the graph for the iteration body.
     *
     * See Utils::iterate, Utils::iterateBoundedStreams and Utils::iterateAndReplayBoundedStreams for how the iteration
     * body can be executed and when execution of the corresponding graph should terminate.
     *
     * Required: the number of feedback variable streams returned by this method must equal the number of variable
     * streams given to this method.
     *
     * @param variableStreams the variable streams.
     * @param dataStreams the data streams.
     * @return a IterationBodyResult.
     */
    IterationBodyResult process(DataStreamList variableStreams, DataStreamList dataStreams);
}

2) Add IterationBodyResult class.

This is a helper class which contains the objects returned by the IterationBody::process(...).

package org.apache.flink.ml.iteration;

/**
 * A helper class that contains the streams returned by the iteration body.
 */
class IterationBodyResult {
    /**
     * A list of feedback variable streams. These streams will only be used during the iteration execution and will
     * not be returned to the caller of the iteration body. It is assumed that the method which executes the
     * iteration body will feed the records of the feedback variable streams back to the corresponding input variable
     * streams.
     */
    DataStreamList feedbackVariableStreams;

    /**
     * A list of output streams. These streams will be returned to the caller of the methods that execute the
     * iteration body.
     */
    DataStreamList outputStreams;

    /**
     * An optional termination criteria stream. If this stream is not null, it will be used together with the
     * feedback variable streams to determine when the iteration should terminate.
     */
    Optional<DataStream<?>> terminationCriteria;
}

3) Add the IterationListener interface.

If an UDF (a.k.a user-defined function) used inside the IterationBody implements this interface, the callbacks on this interface will be invoked when corresponding events happen.

This interface allows users to achieve the following goals:
- Run an algorithm in sync mode, i.e. each subtask will wait for model parameters updates from all other subtasks before reading the aggregated model parameters and starting the next epoch of execution. 
- Emit final output after the iteration terminates.

org.apache.flink.ml.iteration

/**
 * The callbacks defined below will be invoked only if the operator instance which implements this interface is used
 * within an iteration body.
 */
@PublicEvolving
public interface IterationListener<T> {
    /**
     * This callback is invoked every time the epoch watermark of this operator increments. The initial epoch watermark
     * of an operator is 0.
     *
     * The epochWatermark is the maximum integer that meets this requirement: every record that arrives at the operator
     * going forward should have an epoch larger than the epochWatermark. See Java docs in IterationUtils for how epoch
     * is determined for records ingested into the iteration body and for records emitted by operators within the
     * iteration body.
     *
     * If all inputs are bounded, the maximum epoch of all records ingested into this operator is used as the
     * epochWatermark parameter for the last invocation of this callback.
     *
     * @param epochWatermark The incremented epoch watermark.
     * @param context A context that allows emitting side output. The context is only valid during the invocation of
     *                this method.
     * @param collector The collector for returning result values.
     */
    void onEpochWatermarkIncremented(int epochWatermark, Context context, Collector<T> collector);

    /**
     * This callback is invoked after the execution of the iteration body has terminated.
     *
     * See Java doc of methods in IterationUtils for the termination conditions.
     *
     * @param context A context that allows emitting side output. The context is only valid during the invocation of
     *                this method.
     * @param collector The collector for returning result values.
     */
    void onIterationTermination(Context context, Collector<T> collector);

    /**
     * Information available in an invocation of the callbacks defined in the IterationProgressListener.
     */
    interface Context {
        /**
         * Emits a record to the side output identified by the {@link OutputTag}.
         *
         * @param outputTag the {@code OutputTag} that identifies the side output to emit to.
         * @param value The record to emit.
         */
        <X> void output(OutputTag<X> outputTag, X value);
    }
}

4) Add the IterationUtils class.

This class provides APIs to execute an iteration body with the user-provided inputs. This class provides three APIs to run an iteration body, each with different input types (e.g. bounded data streams vs. unbounded data streams) and data replay semantics (i.e. whether to replay the user-provided data streams).

Each of these three APIs provide the functionality as described in the iteration paradigm: Union the feedback variables streams (returned by the iteration body) with the initial variable streams (provided by the user) and use the merged streams as inputs to invoke IterationBody::process(...).

package org.apache.flink.ml.iteration;

/**
 * A helper class to apply {@link IterationBody} to data streams.
 */
@PublicEvolving
public class IterationUtils {
    /**
     * This method can use an iteration body to process records in unbounded data streams.
     *
     * This method invokes the iteration body with the following parameters:
     * 1) The 1st parameter is a list of input variable streams, which are created as the union of the initial variable
     * streams and the corresponding feedback variable streams (returned by the iteration body).
     * 2) The 2nd parameter is the data streams given to this method.
     *
     * The epoch values are determined as described below. See IterationListener for how the epoch values are used.
     * 1) All records in the initial variable streams has epoch=1.
     * 2) All records in the data streams has epoch=MAX_LONG. In this case, records in the data stream won't affect
     * any operator's epoch watermark.
     * 3) For any record emitted by this operator into a non-feedback stream, the epoch of this emitted record = the
     * epoch of the input record that triggers this emission. If this record is emitted by
     * onEpochWatermarkIncremented(), then the epoch of this record = epochWatermark.
     * 4) For any record emitted by this operator into a feedback variable stream, the epoch of the emitted record =
     * min(the epoch of the input record that triggers this emission, MAX_LONG - 1) + 1. If this record is emitted by
     * onEpochWatermarkIncremented(), then the epoch of this record = epochWatermark + 1.
     *
     * The execution of the graph created by the iteration body will not terminate by itself. This is because at least
     * one of its data streams is unbounded.
     *
     * Required:
     * 1) All the init variable streams must be bounded.
     * 2) There is at least one unbounded stream in the data streams list.
     * 3) The parallelism of any stream in the initial variable streams must equal the parallelism of the stream at the
     * same index of the feedback variable streams returned by the IterationBody.
     *
     * @param initVariableStreams The initial variable streams. These streams will be merged with the feedback variable
     *                            streams before being used as the 1st parameter to invoke the iteration body.
     * @param dataStreams The data streams. These streams will be used as the 2nd parameter to invoke the iteration
     *                    body.
     * @param body The computation logic which takes variable/data streams and returns variable/output streams.
     * @return The list of output streams returned by the iteration boy.
     */
    static DataStreamList iterateUnboundedStreams(DataStreamList initVariableStreams, DataStreamList dataStreams, IterationBody body) {...}

    /**
     * This method can use an iteration body to process records in some bounded data streams iteratively until a
     * termination criteria is reached (e.g. the given number of rounds is completed or no further variable update is
     * needed). Because this method does not replay records in the data streams, the iteration body needs to cache those
     * records in order to visit those records repeatedly.
     *
     * This method invokes the iteration body with the following parameters:
     * 1) The 1st parameter is a list of input variable streams, which are created as the union of the initial variable
     * streams and the corresponding feedback variable streams (returned by the iteration body).
     * 2) The 2nd parameter is the data streams given to this method.
     *
     * The epoch values are determined as described below. See IterationListener for how the epoch values are used.
     * 1) All records in the initial variable streams has epoch=1.
     * 2) All records in the data streams has epoch=1.
     * 3) For any record emitted by this operator into a non-feedback stream, the epoch of this emitted record = the
     * epoch of the input record that triggers this emission. If this record is emitted by
     * onEpochWatermarkIncremented(), then the epoch of this record = epochWatermark.
     * 4) For any record emitted by this operator into a feedback variable stream, the epoch of the emitted record = the
     * epoch of the input record that triggers this emission + 1. If this record is emitted by
     * onEpochWatermarkIncremented(), then the epoch of this record = epochWatermark + 1.
     *
     * Suppose there is a coordinator operator which takes all feedback variable streams (emitted by the iteration body)
     * and the termination criteria stream (if not null) as inputs. The execution of the graph created by the
     * iteration body will terminate when all input streams have been fully consumed AND any of the following conditions
     * is met:
     * 1) The termination criteria stream is not null. And the coordinator operator has not observed any new value from
     * the termination criteria stream between two consecutive onEpochWatermarkIncremented invocations.
     * 2) The coordinator operator has not observed any new value from any feedback variable stream between two
     * consecutive onEpochWatermarkIncremented invocations.
     *
     * Required:
     * 1) All the init variable streams and the data streams must be bounded.
     * 2) The parallelism of any stream in the initial variable streams must equal the parallelism of the stream at the
     * same index of the feedback variable streams returned by the IterationBody.
     *
     * @param initVariableStreams The initial variable streams. These streams will be merged with the feedback variable
     *                            streams before being used as the 1st parameter to invoke the iteration body.
     * @param dataStreams The data streams. These streams will be used as the 2nd parameter to invoke the iteration
     *                    body.
     * @param body The computation logic which takes variable/data streams and returns variable/output streams.
     * @return The list of output streams returned by the iteration boy.
     */
    static DataStreamList iterateBoundedStreamsUntilTermination(DataStreamList initVariableStreams, DataStreamList dataStreams, IterationBody body) {...}

    /**
     * This method can use an iteration body to process records in some bounded data streams iteratively until a
     * termination criteria is reached (e.g. the given number of rounds is completed or no further variable update is
     * needed). Because this method replays records in the data streams, the iteration body does not need to cache those
     * records to visit those records repeatedly.
     *
     * This method invokes the iteration body with the following parameters:
     * 1) The 1st parameter is a list of input variable streams, which are created as the union of the initial variable
     * streams and the corresponding feedback variable streams (returned by the iteration body).
     * 2) The 2nd parameter is a list of replayed data streams, which are created by replaying the initial data streams
     * round by round until the iteration terminates. The records in the Nth round will be emitted into the iteration
     * body only if the low watermark of the first operator in the iteration body >= N - 1.
     *
     * The epoch values are determined as described below. See IterationListener for how the epoch values are used.
     * 1) All records in the initial variable streams has epoch=1.
     * 2) The records from the initial data streams will be replayed round by round into the iteration body. The records
     * in the first round have epoch=1. And records in the Nth round have epoch = N.
     * 3) For any record emitted by this operator into a non-feedback stream, the epoch of this emitted record = the
     * epoch of the input record that triggers this emission. If this record is emitted by
     * onEpochWatermarkIncremented(), then the epoch of this record = epochWatermark.
     * 4) For any record emitted by this operator into a feedback stream, the epoch of the emitted record = the epoch
     * of the input record that triggers this emission + 1. If this record is emitted by onEpochWatermarkIncremented(),
     * then the epoch of this record = epochWatermark + 1.
     *
     * Suppose there is a coordinator operator which takes all feedback variable streams (emitted by the iteration body)
     * and the termination criteria stream (if not null) as inputs. The execution of the graph created by the
     * iteration body will terminate when all input streams have been fully consumed AND any of the following conditions
     * is met:
     * 1) The termination criteria stream is not null. And the coordinator operator has not observed any new value from
     * the termination criteria stream between two consecutive onEpochWatermarkIncremented invocations.
     * 2) The coordinator operator has not observed any new value from any feedback variable stream between two
     * consecutive onEpochWatermarkIncremented invocations.
     *
     * Required:
     * 1) All the init variable streams and the data streams must be bounded.
     * 2) The parallelism of any stream in the initial variable streams must equal the parallelism of the stream at the
     * same index of the feedback variable streams returned by the IterationBody.
     *
     * @param initVariableStreams The initial variable streams. These streams will be merged with the feedback variable
     *                            streams before being used as the 1st parameter to invoke the iteration body.
     * @param initDataStreams The initial data streams. Records from these streams will be repeatedly replayed and used
     *                        as the 2nd parameter to invoke the iteration body.
     * @param body The computation logic which takes variable/data streams and returns variable/output streams.
     * @return The list of output streams returned by the iteration boy.
     */
    static DataStreamList iterateAndReplayBoundedStreamsUntilTermination(DataStreamList initVariableStreams, DataStreamList initDataStreams, IterationBody body) {...}
}

5) Add the DataStreamList class.

DataStreamList is a helper class that contains a list of data streams with possibly different elements types.

package org.apache.flink.ml.iteration;

public class DataStreamList {
    // Returns the number of data streams in this list.
    public int size() {...}

    // Returns the data stream at the given index in this list.
    public <T> DataStream<T> get(int index) {...}
}

6) Deprecate the existing DataStream::iterate() and the DataStream::iterate(long maxWaitTimeMillis) methods.

We plan to remove both methods after the APIs added in this doc is ready for production use. This change is needed to decouple the iteration-related APIs from core Flink core runtime  so that we can keep the Flink core runtime as simple and maintainable as possible.

Proposed Changes

In this section, we discuss a few design choices related to the implementation and usage of the proposed APIs.

1) How the feedback edge is supported.

The Flink core runtime can only execute a DAG of operators that does not involve cycles. Thus extra work needs to be done to support feedback edges (which effectively introduces cycles in the data flow).

Similar to the existing iterative API, this FLIP plans to implement the feedback edge using the following approach:

• Automatically insert the HEAD and the TAIL operators as the first and the last operators in the iteration body.
• Co-locate the HEAD and the TAIL operators on the same task manager.
• Have the HEAD and the TAIL operators transmit the records of the feedback edges using an in-memory queue data structure. 

Since all the forward edges have limited buffers, to avoid the deadlocks the feedback queues must have unlimited size. To avoid unlimited memory footprint, when the queued size exceeds a threshold the records would be spilled to the disk. To avoid such spilling the HEAD operators would read the data in a "feedback-first" manner, namely it would always process the feedback records first if there are records from both initial input and feedback edges.

2) How the termination of the iteration execution is determined.

We will add a coordinator operator which takes all feedback variable streams (emitted by the iteration body) and the termination criteria stream (if not null) as inputs. The execution of the graph created by the iteration body will terminate when all input streams have been fully consumed OR any of the following conditions is met:

• The termination criteria stream is not null. And the coordinator operator has not observed any new value from the termination criteria stream between two consecutive onEpochWatermarkIncremented invocations.
• The coordinator operator has not observed any new value from any feedback variable stream between two consecutive onEpochWatermarkIncremented invocations.

TODO: explain how this is implemented.

4) The execution mode that is required to execute the iteration body.

• If all inputs streams are bounded, then the iteration body can be executed in either the stream mode or the batch mode.
• If any input stream is unbounded, then the iteration body must be executed in the stream mode.

5) The requirements of the edge types and parallelism in the IterationBody.

All edges inside the iteration body are required to have the PIPELINE type. If the user-defined iteration body contains an edge that does not have the PIPELINE type, methods that create the subgraph from the iteration body, such as iterateBoundedStreamsUntilTermination, will throw exception upon invocation.

6) Lifetime of the operators inside the iteration body.

With the approach proposed in this FLIP, the operators inside the iteration body are only created once and destroyed after the entire iteration terminates.

In comparison, the existing DataSet::iterate(..) would destroy and re-create the iteration body once for each round of iteration, which in general could introduce more runtime overhead then the approach adopted in this FLIP.

7) How an iteration can resume from the most recent completed epoch after failover.

For any job that is executed in the batch mode, the job can not start from a recent epoch after failover. In other words, if an iterative job fails, it will start from the first epoch of this iteration. Note that the existing DataSet::iterate(...) has the same behavior after job failover.

For any job that is executed in the stream mode, the job can start from a recent epoch after failover. This is achieved by re-using the existing checkpoint mechanism (only available in the stream mode) and additionally checkpointing the values buffered on the feedback edges.

8) How to implement an iterative algorithm in the sync mode.

Definition of sync-mode

An iterative algorithm is run in sync-mode if there exists global epoch, such that at the time a given operator computes its output for the Nth epoch, this operator has received exactly the following records from its input edges:

• We define a feedback loop as a circle composed of exactly 1 feedback edge and arbitrary number of non-feedback edges.
• If an edge is a non-feedback input edge and this edge is part of a feedback loop, then this operator has received all records emitted on this edge for the Nth epoch, without receiving any record for the (N+1)th epoch.
• If an edge is a feedback input edge and this edge is part of a feedback loop, then this operator has received all records emitted on this edge for the (N-1)th epoch, without receiving any record for the Nth epoch.

Solution to run an iterative algorithm in the sync mode

An iterative algorithm will be run in the sync mode if its IterationBody meets the following requirements:

• When any operator within the IterationBody receives values from its input edges, this operator does not immediately emit records to its output.
• Operators inside the IterationBody only compute and emit records to their outputs in the onEpochWatermarkIncremented(...) callback. The emitted records should be computed based on the values received from the input edges up to the invocation of this callback.

See the Appendix section for a proof of why the solution described above could achieve the sync-mode execution as defined above.

9) How to run an iterative algorithm without dumping all user-provided data streams to disk.

As mentioned in the motivation section, the existing DataSet::iterate() always dump the user-provided data streams to disk so that it can replay the data streams regardless of the size of those data streams. Since this is the only available API to do iteration on bounded data streams, there is no way for algorithm developer to get rid of this performance overhead.

In comparison, the iterateBoundedStreamsUntilTermination(...) method proposed in this FLIP allows users to run an iteration body without incurring this disk performance overhead. Developers have the freedom to optimize the performance based on its algorithm and data size, e.g. cache data in memory in a more compact format.

10) How to support operators (e.g. ReduceOperator) that requires bounded inputs in the IterationBody.

TODO: explain it.

To avoid more data is read from the inputs while too much data accumulate inside the iteration, the iteration would first process the feedback data if both side of data is available. 

For termination detection, the iteration would continue until

1. All the inputs are terminated.
2. And there is no records inside the iteration subgraph. 

Then the iteration terminates.

Bounded Iteration

As mentioned in the motivation, the existing dataset iteration API uses the "per-round" semantics: it views the iteration as a repeat execution of the same DAG, thus underlying it would automatically merge the inputs and feedbacks and replay the inputs without feedbacks, and the operators inside the iteration live only for one-round. This might cause bad performance for some algorithms who could cache these data in a more efficient way. 

To avoid this issue, similar to the unbounded iteration, by default we use the "per-iteration" semantics: 

1. Operators inside the iteration would live till the whole iteration is finished.
2. We do not automatically merge the inputs and feedbacks. Instead, we union the original inputs and the feedbacks so that users could decide how the merge them.
3. We do not replay the inputs without feedbacks. Users could decide to how to cache them more efficiently. 

Besides, to cooperate with the "per-round" semantics, previously the iteration is by default synchronous: before the current round fully finished, the feedback data is cached and would not be emitted. Thus it could not support some algorithms like asynchronous regression. To cope with this issue, we view synchronous iteration as a special case of asynchronous iteration with additional synchronization. Thus by default the iteration is asynchronous. 

Based on the above assumption, the API to add iteration to a job is nearly the same compared to the unbounded iteration. The only difference is that bounded iteration supports more sophisticated termination conditions: a function is evaluated when each round ends based on the round or the records of a specified data stream. If it returns true, the iteration would deserts all the following feedback records, ends all the ongoing rounds and finish. 

Since now the operators would live across multiple rounds and multiple rounds might be concurrent, the operators inside the iteration needs to know the rounds of the current record and when one round is fully finished, namely the progress tracking. For example, an operator computes the sum of the records in each rounds would like to add the record to the corresponding partial sum, and when one round is finished, it would emit the sum for this round. To support the progress track, UDFs / operators inside the iteration could implementation `BoundedIterationProgressListener` to acquire the additional information about the progress. 

Based on the progress tracking interface, if users want to implement a synchronous method, some operators inside the subgraph needs to be synchronous: they only emits the records in `onRoundEnd`, namely after all the data of the current round is received. If for the subgraph of iteration body, every path from input to the feedbacks has at least such an operator, then the iteration would be synchronous. 

For users still want to use the iteration with the "per-round" semantics, a utility `forEachRound()` is provided. With the utility users could add a subgraph inside the iteration body that

1. The operators inside the subgraph would live only for one round.
2. If an input stream without feedback is referenced, the input stream would be replayed for each round.

For input stream with feedbacks, we also provide two utility processFunction that automatically merge the original inputs and feedbacks. Both the existing bulk and delta method is supported. Then users would be able to implement a per-round iteration with input.process(bulkCache()).forEachRound(() → {...}).

The API for the bounded iteration is as follows:

Examples

This sections shows how general used ML algorithms could be implemented with the iteration API. 

Offline Training with Bounded Iteration

We would like to first show the usage of the bounded iteration with the linear regression case: the model is Y = XA, and we would like to acquire the best estimation of A with the SGD algorithm. To simplify we assume the parameters could be held in the memory of one task.

The job graph of the algorithm could be shown in the Figure 3: in each round, we use the latest parameters to calculate the update to the parameters: ΔA = ∑(Y - XA)X. To achieve this, the Parameters vertex would broadcast the latest parameters to the Train vertex. Each subtask of the Train vertex holds a part of dataset. Follow the sprite of SGD, it would sample a small batch of training records, and calculate the update with the above equation. Then the Train vertex emit ΔA to the Parameters node to update the parameters.

Figure 3. The JobGraph for the offline training of the linear regression case.

We will start with the synchronous training. The synchronous training requires the updates from all the Train vertex subtask is merged before the next round of training. It could be done by only emit the next round of parameters on the end of round. The code is shown as follows:

public class SynchronousBoundedLinearRegression {
    private static final N_DIM = 50;
    private static final OutputTag<double[]> FINAL_MODEL_OUTPUT_TAG = new OutputTag<double[]>{};

    public static void main(String[] args) {
        DataStream<double[]> initParameters = loadParameters().setParallelism(1);
        DataStream<Tuple2<double[], Double>> dataset = loadDataSet().setParallelism(1);

        int batch = 5;
        int epochEachBatch = 10;

        ResultStreams resultStreams = new BoundedIteration()
            .withBody(new IterationBody(
                @IterationInput("model") DataStream<double[]> model,
                @IterationInput("dataset") DataStream<Tuple2<double[], Double>> dataset
            ) {
                SingleOutputStreamOperator<double[]> parameters = model.process(new ParametersCacheFunction());
                DataStream<double[]> modelUpdate = parameters.setParallelism(1)
                    .broadcast()
                    .connect(dataset)
                    .coProcess(new TrainFunction())
                    .setParallelism(10)

                return new BoundedIterationDeclarationBuilder()
                    .withFeedback("model", modelUpdate)
                    .withOutput("final_model", parameters.getSideOut(FINAL_MODEL_OUTPUT_TAG))
                    .until(new TerminationCondition(null, context -> context.getRound() >= batch * epochEachBatch))
                    .build();
            })
            .build();
        
        DataStream<double[]> finalModel = resultStreams.get("final_model");
        finalModel.print();
    }

    public static class ParametersCacheFunction extends ProcessFunction<double[], double[]>
        implements BoundedIterationProgressListener<double[]> {  
        
        private final double[] parameters = new double[N_DIM];

        public void processElement(double[] update, Context ctx, Collector<O> output) {
            // Suppose we have a util to add the second array to the first.
            ArrayUtils.addWith(parameters, update);
        }

        public void onRoundEnd(int[] round, Context context, Collector<T> collector) {
            collector.collect(parameters);
        }

        public void onIterationEnd(int[] round, Context context) {
            context.output(FINAL_MODEL_OUTPUT_TAG, parameters);
        }
    }

    public static class TrainFunction extends CoProcessFunction<double[], Tuple2<double[], Double>, double[]> implements BoundedIterationProgressListener<double[]> {

        private final List<Tuple2<double[], Double>> dataset = new ArrayList<>();
        private double[] firstRoundCachedParameter;

        private Supplier<int[]> recordRoundQuerier;

        public void setCurrentRecordRoundsQuerier(Supplier<int[]> querier) {
            this.recordRoundQuerier = querier;
        } 

        public void processElement1(double[] parameter, Context context, Collector<O> output) {
            int[] round = recordRoundQuerier.get();
            if (round[0] == 0) {
                firstRoundCachedParameter = parameter;
                return;
            }

            calculateModelUpdate(parameter, output);
        }

        public void processElement2(Tuple2<double[], Double> trainSample, Context context, Collector<O> output) {
            dataset.add(trainSample)
        }

        public void onRoundEnd(int[] round, Context context, Collector<T> output) {
            if (round[0] == 0) {
                calculateModelUpdate(firstRoundCachedParameter, output);
                firstRoundCachedParameter = null;                
            }
        }

        private void calculateModelUpdate(double[] parameters, Collector<O> output) {
            List<Tuple2<double[], Double>> samples = sample(dataset);

            double[] modelUpdate = new double[N_DIM];
            for (Tuple2<double[], Double> record : samples) {
                double diff = (ArrayUtils.muladd(record.f0, parameters) - record.f1);
                ArrayUtils.addWith(modelUpdate, ArrayUtils.multiply(record.f0, diff));
            }

            output.collect(modelUpdate);
        }
    }
}

If instead we want to do asynchronous training, we would need to do the following change:

1. The Parameters vertex would not wait till round end to ensure received all the updates from the iteration. Instead, it would immediately output the current parameters values once it received the model update from one train subtask.
2. To label the source of the update, we would like to change the input type to be Tuple2<Integer, double[]>. The Parameters would only output the new parameters values to the Train task that send the update.

We omit the change to the graph building code since the change is trivial (change the output type and the partitioner to be customized one). The change to the Parameters vertex is the follows:

public static class ParametersCacheFunction extends ProcessFunction<Tuple2<Integer, double[]>, Tuple2<Integer, double[]>>
    implements BoundedIterationProgressListener<double[]> {  
    
    private final double[] parameters = new double[N_DIM];

    public void processElement(Tuple2<Integer, double[]> update, Context ctx, Collector<Tuple2<Integer, double[]>> output) {
        // Suppose we have a util to add the second array to the first.
        ArrayUtils.addWith(parameters, update);
        output.collect(new Tuple2<>(update.f0, parameters))
    }

    public void onIterationEnd(int[] round, Context context) {
        context.output(FINAL_MODEL_OUTPUT_TAG, parameters);
    }
}

Online Training with Unbounded Iteration

Suppose now we would change the algorithm to unbounded iteration, compared to the offline, the differences is that

1. The dataset is unbounded. The Train operator could not cache all the data in the first round.
2. The training algorithm might be changed to others like FTRL. But we keep using SGD in this example since it does not affect showing the usage of the iteration.

We also start with the synchronous case. for online training, the Train vertex usually do one update after accumulating one mini-batch. This is to ensure the distribution of the samples is similar to the global statistics. In this example we omit the complex data re-sample process and just fetch the next several records as one mini-batch. 

The JobGraph for online training is still shown in Figure 1, with the training dataset become unbounded. Similar to the bounded cases, for the synchronous training, the process would be expected like

1. The Parameters broadcast the initialized values on received the input values.
2. All the Train task read the next mini-batch of records, Calculating an update and emit to the Parameters vertex. Then it would wait till received update parameters from the Parameters Vertex before it head to process the next mini-batch.
3. The Parameter vertex would wait received the updates from all the Train tasks before it broadcast the updated parameters. 

Since in the unbounded case there is not the concept of round, and we do update per-mini-batch, thus we could instead use the InputSelectable functionality to implement the algorithm:

public class SynchronousUnboundedLinearRegression {
    private static final N_DIM = 50;
    private static final OutputTag<double[]> MODEL_UPDATE_OUTPUT_TAG = new OutputTag<double[]>{};

    public static void main(String[] args) {
        DataStream<double[]> initParameters = loadParameters().setParallelism(1);
        DataStream<Tuple2<double[], Double>> dataset = loadDataSet().setParallelism(1);

        ResultStreams resultStreams = new UnboundedIteration()
            .withBody(new IterationBody(
                @IterationInput("model") DataStream<double[]> model,
                @IterationInput("dataset") DataStream<Tuple2<double[], Double>> dataset
            ) {
                SingleOutputStreamOperator<double[]> parameters = model.process(new ParametersCacheFunction(10));
                DataStream<double[]> modelUpdate = parameters.setParallelism(1)
                    .broadcast()
                    .connect(dataset)
                    .transform(
                                "operator",
                                BasicTypeInfo.INT_TYPE_INFO,
                                new TrainOperators(50));
                    .setParallelism(10);

                return new UnBoundedIterationDeclarationBuilder()
                    .withFeedback("model", modelUpdate)
                    .withOutput("model_update", parameters.getSideOut(FINAL_MODEL_OUTPUT_TAG))
                    .build();
            })
            .build();
        
        DataStream<double[]> finalModel = resultStreams.get("model_update");
        finalModel.addSink(...)
    }

    public static class ParametersCacheFunction extends ProcessFunction<double[], double[]> {  
        
        private final int numOfTrainTasks;

        private final int numOfUpdatesReceived = 0;
        private final double[] parameters = new double[N_DIM];

        public ParametersCacheFunction(int numOfTrainTasks) {
            this.numOfTrainTasks = numOfTrainTasks;
        }

        public void processElement(double[] update, Context ctx, Collector<O> output) {
            // Suppose we have a util to add the second array to the first.
            ArrayUtils.addWith(parameters, update);
            numOfUpdatesReceived++;

            if (numOfUpdatesReceived == numOfTrainTasks) {
                output.collect(parameters);
                numOfUpdatesReceived = 0;
            }
        }
    }

    public static class TrainOperators extends AbstractStreamOperator<double[]> implements TwoInputStreamOperator<double[], Tuple2<double[], Double>, double[]>, InputSelectable {

        private final int miniBatchSize;

        private final List<Tuple2<double[], Double>> miniBatch = new ArrayList<>();
        private double[] firstRoundCachedParameter;

        public TrainOperators(int miniBatchSize) {
            this.miniBatchSize = miniBatchSize;
        }

        public void processElement1(double[] parameter, Context context, Collector<O> output) {
            calculateModelUpdate(parameter, output);
			miniBatchSize.clear();
        }

        public void processElement2(Tuple2<double[], Double> trainSample, Context context, Collector<O> output) {
            dataset.add(trainSample);
        }

        public InputSelection nextSelection() {
            if (miniBatch.size() < miniBatchSize) {
                return InputSelection.SECOND;
            } else {
                return InputSelection.FIRST;
            }
        }

        private void calculateModelUpdate(double[] parameters, Collector<O> output) {
            double[] modelUpdate = new double[N_DIM];
            for (Tuple2<double[], Double> record : miniBatchSize) {
                double diff = (ArrayUtils.muladd(record.f0, parameters) - record.f1);
                ArrayUtils.addWith(modelUpdate, ArrayUtils.multiply(record.f0, diff));
            }

            output.collect(modelUpdate);
        }
    }
}

Also similar to the bounded case, for the asynchronous training the Parameters vertex would not wait for received updates from all the Train tasks. Instead, it would directly response to the task sending update:

public static class ParametersCacheFunction extends ProcessFunction<Tuple2<Integer, double[]>, Tuple2<Integer, double[]>> {  
    
    private final double[] parameters = new double[N_DIM];

    public void processElement(Tuple2<Integer, double[]> update, Context ctx, Collector<Tuple2<Integer, double[]>> output) {
        ArrayUtils.addWith(parameters, update);
                
        if (update.f0 < 0) {
            // Received the initialized parameter values, broadcast to all the downstream tasks
            for (int i = 0; i < 10; ++i) {
                output.collect(new Tuple2<>(i, parameters))        
            }
        } else {
            output.collect(new Tuple2<>(update.f0, parameters))
        }
    }
}

Implementation Plan

Logically all the iteration types would support both BATCH and STREAM execution mode. However, according to the algorithms' requirements, we would implement 

1. Unbounded iteration + STREAM mode.
2. Bounded iteration + BATCH mode.

Currently we do not see requirements on Bounded iteration + STREAM mode, if there are additional requirement in the future we would implement this mode, and it could also be supported with the current framework. 

Compatibility, Deprecation, and Migration Plan

The API is added as a library inside flink-ml repository, thus it does not have compatibility problem. However, it has some difference with the existing iteration API and the algorithms would need some re-implementation.

For the long run, the new iteration implementation might provide an alternative for the iteration functionality, and we may consider deprecating and removing the existing API to reduce the complexity of core flink code. 

Rejected Alternatives

Naiad has proposed a unified model for watermark mechanism (namely progress tracking outside of the iteration) and the progress tracking inside the iteration. It extends the event time and watermark to be a vector (long timestamp, int[] rounds) and implements a vectorized alignment algorithm. Although Naiad provides an elegant model, the direct implementation on Flink would requires a large amount of modification to the flink runtime, which would cause a lot of complexity and maintenance overhead.  Thus we would choose to implement a simplified version on top of FLINK, as a part of the flink-ml library.

For the iteration DAG build graph, it would be more simpler if we could directly refer to the data stream variables outside of the closure of iteration body. However, since we need to make the iteration DAG creation first happen in the mock execution environment, we could not use these variables directly, otherwise we would directly modify the real environment and won't have chance to add wrappers to the operators.