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Communication-Efficient Policy Gradient Methods for Distributed Reinforcement Learning

Tianyi Chen, Kaiqing Zhang, Georgios B. Giannakis, Tamer Başar

arXiv:1812.03239v3cs.LGcs.MAstat.ML

TL;DR

Distributed RL requires frequent controller–learner exchanges, whose cost and latency can bottleneck performance. LAPG is a communication-cognizant policy-gradient method that preserves PG convergence while reducing communication rounds for heterogeneous learners.

  • Problem

    Distributed RL requires frequent controller–learner exchanges, whose cost and latency can bottleneck performance; prior communication-efficient work had not particularly focused on RL.

    Source: §I · p. 1

  • Method

    LAPG is a communication-cognizant policy-gradient method for distributed RL.

    Source: §VI · p. 8

  • Results

    Roughly O(1/M) communication rounds of PG are needed in the stated heterogeneous case, while LAPG retains PG’s sublinear convergence to a stationary point.

    Source: §IV · pp. 6–7

  • Takeaways & Limitations

    LAPG reduces communication overhead while retaining PG convergence rates when distributed learners are heterogeneous.

    Source: §VI · p. 8

    LAPG requires sufficiently many mini-batch trajectories to obtain low-variance policy gradients.

    Source: §VI · p. 8

Abstract

from arXiv · show

This paper deals with distributed policy optimization in reinforcement learning, which involves a central controller and a group of learners. In particular, two typical settings encountered in several applications are considered: multi-agent reinforcement learning (RL) and parallel RL, where frequent information exchanges between the learners and the controller are required. For many practical distributed systems, however, the overhead caused by these frequent communication exchanges is considerable, and becomes the bottleneck of the overall performance. To address this challenge, a novel policy gradient approach is developed for solving distributed RL. The novel approach adaptively skips the policy gradient communication during iterations, and can reduce the communication overhead without degrading learning performance. It is established analytically that: i) the novel algorithm has convergence rate identical to that of the plain-vanilla policy gradient; while ii) if the distributed learners are heterogeneous in terms of their reward functions, the number of communication rounds needed to achieve a desirable learning accuracy is markedly reduced. Numerical experiments corroborate the communication reduction attained by the novel algorithm compared to alternatives.

I. INTRODUCTION

Distributed RL extends single-learner methods to coordinated learners in multi-agent collaborative and parallel settings. Frequent controller–learner exchanges can make communication cost and latency a performance bottleneck, motivating communication-efficient RL methods.

I. INTRODUCTION

  • Distributed RL covers multi-agent collaborative RL and parallel RL, with a central controller coordinating agents or workers.Collaborative agents seek team-averaged long-term reward; parallel machines address large-scale MDPs.Source: §I · p. 1
  • Controller–learner exchanges collect rewards and local observations or broadcast the policy, and their cost and latency can bottleneck overall performance.The paper names cloud-edge AI, autonomous driving, and IoT applications as examples.Source: §I · p. 1
  • Although communication-efficient supervised learning had attracted interest, prior work had not particularly focused on RL, motivating a general algorithm with convergence guarantees and reduced communication overhead..Source: §I · p. 1

A. Our contributions

The paper proposes Lazily Aggregated Policy Gradient (LAPG), a policy-gradient method for distributed RL. It preserves vanilla PG’s convergence order while reducing communication rounds for heterogeneous learners.

A. Our contributions

  • LAPG achieves the same order of convergence rate, and thus iteration complexity, as vanilla PG under standard conditions.The paper also reports sublinear convergence to a stationary point under its adaptive communication rules.Source: A. Our contributions · p. 1
  • LAPG reduces communication rounds needed for desirable learning accuracy when learners differ in reward functions and initial states.Source: A. Our contributions · p. 1
  • In certain learning settings, LAPG requires only O(1/M) communication of PG, where M is the number of learners.Source: A. Our contributions · p. 1
  • On the cooperative navigation benchmark, neural-network-policy experiments corroborate that LAPG considerably reduces communication required by PG.Source: A. Our contributions · p. 1

B. Related work

Prior work developed policy-gradient methods for single learners and distributed RL across multi-agent and parallel settings, but did not address communication efficiency in distributed RL. LAPG is distinguished from supervised-learning approaches by its handling of stochastic, potentially biased gradients and time-varying data distributions.

B. Related work

  • Policy-gradient variants address convergence speed, variance, nonlinear policies, continuous actions, and policy improvement, but the cited methods were developed for single learners.The passage describes REINFORCE [22] and G(PO)MDP [23] as Monte Carlo trajectory-based methods.Source: B. Related work · p. 2
  • Distributed multi-agent RL includes guaranteed tabular methods, networked QD-learning, decentralized actor-critic, and empirical deep methods –.Source: B. Related work · p. 2
  • Parallel RL has used Map Reduce, massively distributed frameworks, and asynchronous algorithms [12], but these works did not tackle communication efficiency.Source: B. Related work · p. 2
  • Existing communication-efficient methods do not directly fit stochastic, nonconvex PG-based distributed RL; some reduce bandwidth per exchange rather than communication rounds.Event-triggered control typically uses nonadaptive triggers and seeks longer intervals between control actions while ensuring convergence.Source: B. Related work · p. 2
  • Compared with LAG [21] for supervised learning, LAPG handles stochastic settings with possibly biased gradients and uses a modified communication rule with probabilistic analysis.RL also introduces non-stationarity because the data-sampling distribution depends on time-varying parameters.Source: B. Related work · p. 2
  • The authors characterize communication-efficient distributed RL as a challenging, less explored area.Source: B. Related work · p. 2

II. DISTRIBUTED REINFORCEMENT LEARNING

This section introduces background on distributed RL and plain-vanilla policy-gradient methods applicable to distributed RL tasks.

II. DISTRIBUTED REINFORCEMENT LEARNING

  • The section presents essential background for distributed RL and plain-vanilla PG methods applicable to its tasks.Source: §II · p. 2
  • Distributed RL is one of the two background topics identified for the section.Source: §II · p. 2
  • Plain-vanilla PG methods are the other background topic identified for the section.Source: §II · p. 2

A. Problem statement

The problem is to minimize the infinite-horizon discounted loss aggregated across learners under a distributed MDP. The formulation covers collaborative multi-agent RL and parallel RL, which differ in how learners are coupled.

A. Problem statement

  • The distributed objective aggregates each learner’s discounted loss, with trajectories determined by the policy and the underlying MDP.The MDP is specified by state and action spaces, transition kernels, a discount factor, an initial-state distribution, and learner-specific losses.Source: A. Problem statement · pp. 2–3
  • In collaborative multi-agent RL, agents share a global state, use local action spaces, and jointly determine transitions and each agent’s loss.The objective is formed over joint state-action trajectories.Source: A. Problem statement · p. 3
  • In parallel RL, workers solve independent instances of an identical MDP with shared state, action, and transition spaces, but differing losses and initial-state distributions.Workers are intertwined by learning a common policy rather than by joint transitions or shared losses.Source: A. Problem statement · p. 3
  • The considered distributed RL setting assumes globally observable state but private reward functions, unlike distributed control settings where learners do not all observe the global state.The private rewards make policy-gradient acquisition a distributed task.Source: A. Problem statement · p. 3

B. Policy gradient methods

Policy gradient methods search over parameterized policies, turning policy optimization into parameter optimization. In distributed RL, stochastic gradient estimates support this approach, but collecting every learner’s gradient at each iteration creates communication overhead.

B. Policy gradient methods

  • Policy gradient methods parameterize a policy by θ, reducing the search for a best-performing policy to optimization over parameters.The parameterized policy is written π(·|s; θ); its mean function may be a neural network or a linear function of θ.Source: B. Policy gradient methods · pp. 3–4
  • When the MDP is unknown or the exact expectation is difficult to compute, G(PO)MDP supplies an unbiased stochastic policy-gradient estimate with lower variance than REINFORCE.Its variance can still be high, requiring small step sizes and sufficiently many iterations for convergence.Source: B. Policy gradient methods · p. 4
  • Vanilla distributed policy gradient requires all learners’ gradients to be uploaded to form the objective gradient, creating communication overhead across iterations.The paper motivates communication-efficient schemes as a response to this repeated exchange.Source: B. Policy gradient methods · p. 4

III. COMMUNICATION-EFFICIENT DISTRIBUTED POLICY GRADIENT METHODS

The section introduces LAPG, which updates the distributed policy while skipping some learner communications by refining the previous aggregate with newly uploaded gradient innovations. Its selection rule is designed to balance communication savings against optimization progress and gradient-estimation error.

III. COMMUNICATION-EFFICIENT DISTRIBUTED POLICY GRADIENT METHODS

  • LAPG avoids requesting fresh batch gradients from every learner by refining the previous aggregate with current innovations and reused gradients from non-uploading learners.The controller stores the prior aggregate; participating learners upload the difference between current and previously evaluated gradients, whose reference policy copies can differ by learner.Source: §III · pp. 4–5
  • The LAPG progress analysis accounts for descent, finite-horizon approximation error, communication-skipping error, and stochastic-gradient variance.The section describes controlling skipped-communication error relative to gradient magnitude and stochastic variance; its descent lemma assumes an L-smooth objective and α ≤ 1/L.Source: §III · p. 5
  • The stochastic-gradient deviation is bounded with high probability under the stated assumptions, with its bound depending mainly on trajectory count and logarithmically on confidence and iteration count.The section identifies the mini-batch gradient variance as a quantity used in the communication condition.Source: §III · p. 5
  • Learners communicate when their current gradient has enough innovation relative to their most recently uploaded gradient, rather than minimizing the number selected per iteration.A myopic selection of as few learners as possible may increase iterations and total communication rounds.Source: §III · p. 5
  • Implementing LAPG adds storage of each learner’s most recently uploaded gradient and checking the communication condition to the policy-gradient procedure.The algorithm broadcasts policy parameters; only learners satisfying the condition upload, after which the controller updates the global policy.Source: §III · pp. 5–6
  • The authors identify unbiased gradient estimation as a requirement of the analysis, making it more suited to episodic settings than continuing tasks.Extending the analysis to continuing tasks is left for future work.Source: §III · p. 6

IV. MAIN RESULTS

LAPG retains vanilla PG’s sublinear convergence while reducing communication rounds under stated learner-heterogeneity conditions. Its communication analysis relates upload frequency to task hardness and shows a large reduction in a heterogeneous example.

Theorem 1 (iteration complexity)

  • With adaptive communication rules, LAPG achieves sublinear convergence to a stationary point, matching plain-vanilla PG’s convergence order.The result is stated under Assumptions 1 and 2.Source: §IV · p. 6

Lemma 4 (lazy communication)

  • Learner communication frequency is proportional to task hardness; under Lemma 4’s condition, a learner uploads at most 1/(d + 1) of the time.Larger trigger constants and a smaller stepsize reduce communication frequency, but generally require more iterations for a desired accuracy.Source: §IV · p. 6

Theorem 2 (communication complexity)

  • Under the stated heterogeneity condition, LAPG requires fewer communication rounds than PG to reach the target policy-gradient error.The comparison holds with the theorem’s specified parameter choices.Source: §IV · p. 7
  • In the stated heterogeneous example, LAPG requires roughly O(1/M) as many communication rounds as plain-vanilla PG.The example has M−1 learners with L_m = O(1) and one learner with L_M = O(M^2).Source: §IV · p. 7
  • The theoretical communication improvement depends on somewhat restrictive problem-parameter conditions, although the experiments show gains with the default ξ = 1/D.The stated caveat concerns the parameter dependence of Theorem 2’s improved communication complexity.Source: §IV · p. 7

V. NUMERICAL TESTS

Across parallel and multi-agent Cooperative Navigation tests with two and five agents, LAPG converges in the same number of iterations as PG while requiring fewer communication rounds.

V. NUMERICAL TESTS

  • Cooperative Navigation tasks use two or five agents, globally observable states, and agent-specific rewards that vary with targets, collisions, and positive scaling coefficients.Parallel learners solve independent tasks; in multi-agent RL, learners solve the shared task.Source: §V · pp. 7–8
  • Across parallel and multi-agent tests, LAPG converges in the same number of iterations as PG while requiring fewer communication rounds.Figures 5 and 6 cover iteration and communication complexity for two-agent and five-agent multi-agent RL, respectively.Source: Figure 5 · p. 8, Figure 6 · p. 8, §V · p. 8
  • The tests compare LAPG and PG using both G(PO)MDP and REINFORCE gradient estimators, with five Monte Carlo runs per reported average.Each run uses 10 batch episodes, a discount factor of 0.99, and 20 iterations per episode.Source: §V · p. 8

VI. CONCLUSIONS

LAPG targets communication reduction without changing PG’s convergence rate, while the preliminary lemmas bound policy-gradient deviations and finite-horizon approximation error.

VI. CONCLUSIONS

  • LAPG achieves the same order of convergence rate as vanilla PG and reduces communication rounds when distributed learners are heterogeneous.The conclusion notes that low-variance policy gradients require sufficiently many mini-batch trajectories; future work will consider reusing outdated trajectories and decentralized settings.Source: §VI · p. 8

A. Preliminary lemmas

  • The preliminary lemmas bound the discrepancy between the finite-horizon policy-gradient approximation and its corresponding version.The proof uses bounded loss and score-function assumptions.Source: A. Preliminary lemmas · p. 8
  • A separate preliminary lemma bounds the difference between policy gradients for the infinite-horizon problem and its finite-horizon approximation.The stated bound relies on assumptions bounding the loss and score functions.Source: A. Preliminary lemmas · p. 9

B. Proof of Lemma 1

The appendix proofs establish the descent, concentration, smoothness, iteration-complexity, and communication-frequency claims used in the main analysis.

B. Proof of Lemma 1

  • Combining the LAPG update with bounds on its gradient terms establishes the claim of Lemma 1.The proof rewrites an inner product and combines the resulting inequalities.Source: B. Proof of Lemma 1 · p. 9

C. Proof of Lemma 2

  • Lemma 2’s policy-gradient concentration result follows from a martingale concentration inequality and the bounded policy-gradient deviation.The cited inequality assumes a bounded vector-valued martingale difference sequence.Source: C. Proof of Lemma 2 · pp. 9–10

D. Proof of Lemma 3

  • The proof of Lemma 3 bounds differences in the objective and policy gradients to establish their Lipschitz constants.It uses trajectory notation and the mean-value theorem.Source: D. Proof of Lemma 3 · pp. 10–11

E. Proof of Theorem 1

  • Theorem 1’s proof establishes that suitable T, K, and N choices yield the stated iteration-complexity guarantee.The proof combines finite-horizon truncation error and gradient concentration results.Source: E. Proof of Theorem 1 · p. 11

F. Proof of Lemma 4

  • Under condition (20), each learner communicates at most every other d iterations, with probability at least 1−2δ across all K iterations.This follows from the communication trigger condition and a union bound.Source: F. Proof of Lemma 4 · p. 12

G. Proof of Theorem 2

The proof compares LAPG with PG in iteration and communication cost, then shows that the total-communication bound holds when the stated parameter condition is satisfied.

G. Proof of Theorem 2

  • For sufficiently large T and N, LAPG needs (1−3Dξ)−1 times PG’s iterations to reach the same ϵ-gradient error, with probability 1−2δ.The proof assumes the leading terms in the bounds dominate the remaining error terms.Source: G. Proof of Theorem 2 · p. 12
  • LAPG’s average communication rounds per iteration are (1−∆¯C(h; {γd})) times PG’s, with probability 1−2δ.Combining this with the iteration comparison yields the total-communication bound.Source: G. Proof of Theorem 2 · p. 12
  • Under the stated condition, Theorem 2 gives C_LAPG(ϵ) ≤ C_PG(ϵ) with probability 1−4δ.The condition is given in (65); the communication-round comparison is derived from the average rounds per iteration and the iteration count.Source: G. Proof of Theorem 2 · pp. 12–13

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