Expected Policy Gradients (1706.05374v6)

Abstract: We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates across the action when estimating the gradient, instead of relying only on the action in the sampled trajectory. We establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. We also prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and, for the Gaussian case, with no computational overhead. Finally, we show that it is optimal in a certain sense to explore with a Gaussian policy such that the covariance is proportional to the exponential of the scaled Hessian of the critic with respect to the actions. We present empirical results confirming that this new form of exploration substantially outperforms DPG with the Ornstein-Uhlenbeck heuristic in four challenging MuJoCo domains.

• The paper introduces a general policy gradient theorem that unifies stochastic and deterministic approaches in reinforcement learning.
• It demonstrates that integrating over actions notably reduces variance in gradient estimates, achieving efficiency for Gaussian policies.
• Empirical validation in MuJoCo environments shows that EPG outperforms traditional methods by optimizing exploration in continuous action settings.

Overview of Expected Policy Gradients

The paper "Expected Policy Gradients" by Kamil Ciosek and Shimon Whiteson introduces Expected Policy Gradients (EPG), a novel method that unifies the existing frameworks of Stochastic Policy Gradients (SPG) and Deterministic Policy Gradients (DPG) in the field of reinforcement learning (RL). The proposal is inspired by Expected SARSA, a method for reducing the variance of the estimated action value in Temporal Difference learning. EPG achieves this unification by integrating over possible actions when estimating the gradient, rather than focusing solely on the actions sampled during the trajectory.

Key Contributions

1. General Policy Gradient Theorem: The authors establish a comprehensive policy gradient theorem that encapsulates both stochastic and deterministic policy gradient theorems as particular instances. This theorem simplifies the theoretical landscape of policy gradient methods by providing a unified framework.
2. Variance Reduction in Gradient Estimates: EPG significantly reduces the variance in policy gradient estimates, a notable advantage over SPG and DPG, without necessitating deterministic policies. For Gaussian policies, this reduction is obtained with no additional computational cost compared to SPG.
3. Optimal Exploration Policy: The paper demonstrates that the optimal exploration policy, in a specific sense, for maximizing learned performance is Gaussian with a covariance matrix proportional to the exponential of the scaled Hessian of the critic with respect to actions. This finding is crucial as it addresses the challenge of efficient exploration in RL, particularly within continuous action spaces.
4. Empirical Validation: The efficacy of EPG is empirically validated across four challenging MuJoCo environments, where it exhibited superior performance to DPG using the Ornstein-Uhlenbeck exploration heuristic. This supports the claim that EPG facilitates better exploration strategies.

Practical and Theoretical Implications

From a practical perspective, EPG offers an efficient mechanism for reducing the variance associated with policy gradient estimates. This is particularly valuable in scenarios where sampling new trajectories is computationally expensive. By minimizing variance without increasing computational overhead, EPG enhances sample efficiency, thereby accelerating the learning process in environments with large state-action spaces.

Theoretically, the generalization of policy gradients to include both deterministic and stochastic frameworks under a single umbrella theorem provides new insights into RL methodologies. This synthesis can potentially lead to more robust and adaptable RL algorithms that leverage the strengths of both stochastic and deterministic approaches while mitigating their individual weaknesses.

Future Developments in AI

EPG's approach to variance reduction and efficient exploration could stimulate advancements in algorithm design for environments characterized by large or continuous action spaces. Future research could further investigate the integration of EPG with advanced function approximators like deep neural networks, examining its effectiveness and scalability in even more complex and high-dimensional RL problems.

Moreover, the exploration strategies derived from the Hessian of the critic could be explored in conjunction with other optimization techniques to improve policy convergence rates in dynamic and uncertain environments. Additionally, the theoretical framework laid out in this work might inspire new variants of policy gradients that incorporate uncertainty quantification and risk-sensitive decision-making, expanding the applicability of RL in safety-critical domains.

Overall, EPG represents a promising advancement in the field of reinforcement learning, bridging a significant gap between stochastic and deterministic methodologies and paving the way for future innovations in this rapidly evolving area of AI.