A Prototype of Parameter Server

Introduction

As specified in SPARK-4590,it would be very helpful to integrate parameter server into Spark for machine learning algorithms, especially for those with ultra high dimensions features.

After carefully studying the design doc of Parameter Servers,and the paper of Factorbird, we proposed a prototype of Parameter Server on Spark(Ps-on-Spark), with several key design concerns:

• User friendly interface
  Careful investigation is done to most existing Parameter Server systems(including: petuum, parameter server, paracel) and a user friendly interface is design by absorbing essence from all these system.

• Prototype of distributed array
  IndexRDD (see SPARK-4590) doesn't seem to be a good option for distributed array, because in most case, the #key updates/second is not be very high.
  So we implement a distributed HashMap to store the parameters, which can be easily extended to get better performance.

• Minimal code change
  Quite a lot of effort in done to avoid code change of Spark core. Tasks which need parameter server are still created and scheduled by Spark's scheduler. Tasks communicate with parameter server with a client object, through akka or netty.

With all these concerns we propose the following architecture:

Architecture

Data is stored in RDD and is partitioned across workers. During each iteration, each worker gets parameters from parameter server then computes new parameters based on old parameters and data in the partition. Finally each worker updates parameters to parameter server.Worker communicates with parameter server through a parameter server client,which is initialized in `TaskContext` of this worker.

The current implementation is based on YARN cluster mode,
but it should not be a problem to transplanted it to other modes.

Interface

We refer to existing parameter server systems(petuum, parameter server, paracel) when design the interface of parameter server.

`PSClient` provides the following interface for workers to use:

//  get parameter indexed by key from parameter server
def get[T](key: String): T

// get multiple parameters from parameter server
def multiGet[T](keys: Array[String]): Array[T]

// add parameter indexed by `key` by `delta`, 
// if multiple `delta` to update on the same parameter,
// use `reduceFunc` to reduce these `delta`s frist.
def update[T](key: String, delta: T, reduceFunc: (T, T) => T): Unit

// update multiple parameters at the same time, use the same `reduceFunc`.    
def multiUpdate(keys: Array[String], delta: Array[T], reduceFunc: (T, T) => T: Unit
    
// advance clock to indicate that current iteration is finished.
def clock(): Unit
 
// block until all workers have reached this line of code.
def sync(): Unit

`PSContext` provides following functions to use on driver:

// load parameters from existing rdd.
def loadPSModel[T](model: RDD[String, T]) 

// fetch parameters from parameter server to construct model.
def fetchPSModel[T](keys: Array[String]): Array[T]

A new function has been add to `RDD` to run parameter server tasks:

// run the provided `func` on each partition of this RDD. 
// This function can use data of this partition(the first argument) 
// and a parameter server client(the second argument). 
// See the following Logistic Regression for an example.
def runWithPS[U: ClassTag](func: (Array[T], PSClient) => U): Array[U]
   

Example

Here is an example of using our prototype to implement logistic regression:

def train(
    sc: SparkContext,
    input: RDD[LabeledPoint],
    numIterations: Int,
    stepSize: Double,
    miniBatchFraction: Double): LogisticRegressionModel = {
    
    // initialize weights
    val numFeatures = input.map(_.features.size).first()
    val initialWeights = new Array[Double](numFeatures)

    // initialize parameter server context
    val pssc = new PSContext(sc)

    // load initialized weights into parameter server
    val initialModelRDD = sc.parallelize(Array(("w", initialWeights)), 1)
    pssc.loadPSModel(initialModelRDD)

    // run logistic regression algorithm on input data   
    input.runWithPS((arr, client) => {
      val sampler = new BernoulliSampler[LabeledPoint](miniBatchFraction)
      
      // for each iteration, compute delta and update weights
      for (i <- 0 to numIterations) {
        // get weights from parameter server
        val weights = Vectors.dense(client.get[Array[Double]]("w"))

        sampler.setSeed(i + 42)
        // for each sample point, compute delta and update weights
        sampler.sample(arr.toIterator).foreach { point =>
          // compute delta
          val data = point.features
          val label = point.label
          val margin = -1.0 * dot(data, weights)
          val multiplier = (1.0 / (1.0 + math.exp(margin))) - label
          val delta = Vectors.dense(new Array[Double](numFeatures))
          axpy((-1) * stepSize / math.sqrt(i + 1) * multiplier, data, delta)

          // update weights
          client.update("w", delta.toArray, (d1, d2) => {
            d1.zip(d2).map((a, b) => a + b)
          })
        }
        
        // end of current iteration
        client.clock()
      }
    })

    // fetch weights from parameter server
    val weights = Vectors.dense(pssc.fetchPSModel[Array[Double]](Array("w"))(0))
    val intercept = 0.0

    // construct LogisiticRegressionModel
    new LogisticRegressionModel(weights, intercept).clearThreshold()
}

The above code can be run on current PS-on-Spark implementation.

Other considerations

The current implementation is just a prototype and we will try to improve it in the following directions:

Consistency protocol

Currently we have just implemented BSP protocol. And SSP consistency will be added soon.

Model partition across servers

Currently all the parameters are stored on a single server. Parameters should be partitioned across multiple servers when the parameter size get large. Parameter server client should route request to different servers accordingly.

Performance optimizing

To get better performance, client can cache parameter servers and store updates through operation log(as petuum does). There may be some other ways to improve performance.

Fault Recovery

When a parameter server crashes, it should be restarted on another node. Data of a parameter server should be periodically checkpointed so it can be transfered when a server is restarted.When a task is restarted, it should not rerun finished iterations.

We would like to see parameter server integrated into Spark soon and hope this help other Spark users who need parameter server. As specified above, there is still much work to be done so any comments are welcome.