Towards Understanding Asynchronous Advantage Actor-critic: Convergence and Linear Speedup
This work provides foundational theoretical understanding for the A3C algorithm, a widely used reinforcement learning method, by proving its convergence and the benefits of parallelism for researchers and practitioners in reinforcement learning.
This paper provides a theoretical analysis of the Asynchronous Advantage Actor-critic (A3C) algorithm, establishing non-asymptotic convergence guarantees under both i.i.d. and Markovian sampling. It demonstrates that A3C achieves a sample complexity of O(ε^(-2.5)/N) per worker, showing a linear speedup compared to two-timescale AC, which has a complexity of O(ε^(-2.5)).
Asynchronous and parallel implementation of standard reinforcement learning (RL) algorithms is a key enabler of the tremendous success of modern RL. Among many asynchronous RL algorithms, arguably the most popular and effective one is the asynchronous advantage actor-critic (A3C) algorithm. Although A3C is becoming the workhorse of RL, its theoretical properties are still not well-understood, including its non-asymptotic analysis and the performance gain of parallelism (a.k.a. linear speedup). This paper revisits the A3C algorithm and establishes its non-asymptotic convergence guarantees. Under both i.i.d. and Markovian sampling, we establish the local convergence guarantee for A3C in the general policy approximation case and the global convergence guarantee in softmax policy parameterization. Under i.i.d. sampling, A3C obtains sample complexity of $\mathcal{O}(ε^{-2.5}/N)$ per worker to achieve $ε$ accuracy, where $N$ is the number of workers. Compared to the best-known sample complexity of $\mathcal{O}(ε^{-2.5})$ for two-timescale AC, A3C achieves \emph{linear speedup}, which justifies the advantage of parallelism and asynchrony in AC algorithms theoretically for the first time. Numerical tests on synthetic environment, OpenAI Gym environments and Atari games have been provided to verify our theoretical analysis.