Stochastic Variance-Reduced Policy Gradient (1806.05618v1)

Abstract: In this paper, we propose a novel reinforcement- learning algorithm consisting in a stochastic variance-reduced version of policy gradient for solving Markov Decision Processes (MDPs). Stochastic variance-reduced gradient (SVRG) methods have proven to be very successful in supervised learning. However, their adaptation to policy gradient is not straightforward and needs to account for I) a non-concave objective func- tion; II) approximations in the full gradient com- putation; and III) a non-stationary sampling pro- cess. The result is SVRPG, a stochastic variance- reduced policy gradient algorithm that leverages on importance weights to preserve the unbiased- ness of the gradient estimate. Under standard as- sumptions on the MDP, we provide convergence guarantees for SVRPG with a convergence rate that is linear under increasing batch sizes. Finally, we suggest practical variants of SVRPG, and we empirically evaluate them on continuous MDPs.

• The paper introduces the SVRPG algorithm, which applies Stochastic Variance-Reduced Gradient (SVRG) techniques to reinforcement learning to address high variance in policy gradient methods.
• SVRPG provides theoretical convergence guarantees, demonstrating an O(1/T) rate, and incorporates practical variants like adaptive step size for real-world application.
• Empirical validation on continuous control tasks shows that SVRPG achieves improved convergence rates and stability compared to existing policy gradient methods.

Stochastic Variance-Reduced Policy Gradient: Insights and Implications

The paper introduces a novel reinforcement learning (RL) algorithm, Stochastic Variance-Reduced Policy Gradient (SVRPG), which is designed to address some of the challenges faced by traditional policy gradient methods. This algorithm extends the Stochastic Variance-Reduced Gradient (SVRG) methodology, widely known for its efficacy in supervised learning, to the domain of RL, particularly for solving continuous Markov Decision Processes (MDPs).

Overview

SVRPG is motivated by the need to reduce the variance in policy gradient methods, which is a significant issue due to the stochastic nature of RL environments. The traditional policy gradient methods suffer from high variance estimates, which impacts convergence and the efficiency of the learning process. SVRPG seeks to mitigate these problems by leveraging SVRG-like techniques while taking into account specific challenges unique to RL, such as non-concave objectives, data sampling influenced by policy changes, and the necessity of unbiased gradient estimates.

Core Contributions

1. Variance Reduction: SVRPG incorporates a variance reduction mechanism based on SVRG, involving alternating between full gradient computations and stochastic samples to correct the gradient estimate. This approach is crucial for RL, where sampling directly from the environment is expensive.
2. Convergence Guarantees: The paper provides theoretical convergence guarantees for SVRPG under standard RL assumptions, demonstrating that the algorithm can achieve a convergence rate consistent with that of SVRG in supervised learning, specifically $O(\nicefrac{1}{T})$ with increasing batch sizes $N$ and $B$.
3. Practical Variants and Implementation: Practical implementations of SVRPG are discussed, including adaptive step size adjustment using ADAM and epoch size settings for efficient learning. A self-normalized importance sampling approach is also proposed to address the variance introduced by policy-dependent sampling shifts.
4. Empirical Validation: SVRPG is empirically validated on various continuous RL tasks, including Cart-pole balancing and locomotion tasks like Swimmer and Half-Cheetah using MuJoCo. The results indicate that SVRPG offers improved convergence rates and stability in comparison to existing policy gradient methods, even when combined with baselines.

Implications

The proposed SVRPG algorithm has significant implications for the future of reinforcement learning:

• Practical Efficiency: For applications involving expensive data collection, such as robotic control and simulation environments, SVRPG offers a more practical approach due to its variance reduction capabilities. This reduces the need for large sample sizes, facilitating faster and more cost-effective learning.
• Extension to Other Complex Problems: The convergence guarantees and empirical results suggest that SVRPG could be extended to tackle more complex non-linear control problems and multi-dimensional action spaces, possibly improving the robustness of RL applications across various domains.
• Integration with Actor-Critic and Baselines: The potential integration of SVRPG with actor-critic frameworks and variance-reduction baselines could further enhance efficiency. This opens avenues for developing algorithms that combine multiple variance-reduction techniques, each tackling different aspects of the RL problem.

Future Directions

Future research could explore adapting SVRPG to handle adaptive variance in policies, enhancing its applicability to more dynamic environments. Additionally, exploring theoretical extensions to multi-variate Gaussian policies and other non-linear policy representations may provide deeper insights and broader applicability of the algorithm. Lastly, adaptive batch size mechanisms could be investigated to optimize the trade-off between variance reduction and computational efficiency dynamically.

Overall, SVRPG represents a significant proposal in applying SVRG techniques within reinforcement learning, showcasing the opportunities and challenges of cross-pollinating ideas from supervised learning to reinforcement learning, potentially paving the way for more efficient and robust RL solutions.