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Equivalence Between Policy Gradients and Soft Q-Learning (1704.06440v4)

Published 21 Apr 2017 in cs.LG

Abstract: Two of the leading approaches for model-free reinforcement learning are policy gradient methods and $Q$-learning methods. $Q$-learning methods can be effective and sample-efficient when they work, however, it is not well-understood why they work, since empirically, the $Q$-values they estimate are very inaccurate. A partial explanation may be that $Q$-learning methods are secretly implementing policy gradient updates: we show that there is a precise equivalence between $Q$-learning and policy gradient methods in the setting of entropy-regularized reinforcement learning, that "soft" (entropy-regularized) $Q$-learning is exactly equivalent to a policy gradient method. We also point out a connection between $Q$-learning methods and natural policy gradient methods. Experimentally, we explore the entropy-regularized versions of $Q$-learning and policy gradients, and we find them to perform as well as (or slightly better than) the standard variants on the Atari benchmark. We also show that the equivalence holds in practical settings by constructing a $Q$-learning method that closely matches the learning dynamics of A3C without using a target network or $\epsilon$-greedy exploration schedule.

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Authors (3)
  1. John Schulman (43 papers)
  2. Xi Chen (1036 papers)
  3. Pieter Abbeel (372 papers)
Citations (328)

Summary

Analyzing the Equivalence Between Policy Gradients and Soft Q-Learning

The paper at hand explores a critical link between two significant methodologies in the domain of model-free reinforcement learning (RL): policy gradient (PG) methods and Q-learning (QL) methods. This investigation specifically focuses on the equivalence of these methods in the context of entropy-regularized reinforcement learning.

The core assertion presented is that soft Q-learning, an entropy-regularized variant of Q-learning, is fundamentally equivalent to a policy gradient method. This equivalence is demonstrated by showing that Q-learning, under certain conditions, effectively performs updates that mirror those of policy gradient methods. This insight is encapsulated in the observation that soft Q-learning can be interpreted as a policy gradient term accompanied by a baseline-error-gradient term linked to value function fitting, analogous to actor-critic methodologies such as Asynchronous Advantage Actor-Critic (A3C).

Methodological Insights

The paper explores a detailed mathematical analysis to establish this equivalence. The authors leverage the entropy-regularized optimization framework to illuminate how soft Q-learning maps onto policy gradient updates. Specifically, they reveal that gradients utilized in n-step Q-learning mirror gradients in n-step policy gradient methods, highlighting the accuracy of policy gradient implementations even within complex environments.

Furthermore, an exploration into natural policy gradients reveals another perspective on the soft Q-learning paradigm. Notably, the text describes a connection between Q-learning, employing either batch updates or replay buffers, and natural policy gradient methodologies. This relationship is elucidated through a regression framework in which the value function is approximated via a damped least squares problem, showcasing the broader implications of this equivalence beyond mere gradient strategies.

Experimental Findings

The empirical evaluations underscore the theoretical findings, affirming the practical viability of applying entropy-regularized methods across challenging benchmarks like the Atari games. The results elucidate that both policy gradients and soft Q-learning can achieve comparable or superior performance against traditional, non-regularized variants. Notably, the experiments demonstrate this equivalence holds even with approximated gradients and neural network architectures, supporting implementation in diverse real-world scenarios.

The researchers also address specific conditions where the equivalence is prominent, emphasizing that the scaling of the coefficient in value function updates plays a critical role. The standard implementation in soft Q-learning implicitly weighs value function errors more than typically handled in policy gradient settings, which is a noteworthy operational adjustment suggested by this research.

Theoretical and Practical Implications

This work provides compelling theoretical underpinnings that could impact future RL model design and implementation. By presenting concrete connections between soft Q-learning and policy gradient methodologies, it offers novel insights into the efficiency and robustness of learning processes in environments rich with stochastic dynamics. Practically, these insights afford opportunities for more effective algorithm tuning where choosing between these two approaches might become less about performance trade-offs and more about situational suitability.

Future Directions

While this paper establishes a foundational equivalence, further exploration into different parameterizations and exploration strategies, such as adaptive entropy coefficients, might yield deeper insights. Additionally, extending these findings to other policy-based and value-based frameworks could broaden the applicability and deepen the understanding of RL methodologies.

Overall, the paper lays a robust groundwork for contemplating the intertwined nature of policy gradients and soft Q-learning, presenting a refined lens through which to examine and leverage these powerful RL techniques.

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