Finite Memory Q-Function Approach Bridges Theory and Practice in Reinforcement Learning

A team of machine learning researchers has introduced a new reinforcement learning algorithm that makes policy mirror descent—a theoretically sound but computationally demanding method—practical for real-world applications.

The Challenge with Exact Policy Mirror Descent#

Policy Mirror Descent (PMD) has become an influential framework in reinforcement learning because it smooths out errors that naturally arise when agents learn from imperfect function approximators. The method works by regularizing policy updates using a Kullback-Leibler divergence penalty, which constrains how much the agent's behavior can shift between successive learning steps.

In theory, PMD requires maintaining a sum across all prior Q-functions—estimates of long-term reward values. This requirement proves impractical in most real scenarios, as storing and processing every historical estimate becomes memory-prohibitive and computationally expensive. Researchers have resorted to shortcuts like natural policy gradients or actor-critic methods, but these approximations can introduce their own errors into the policy update process.

The StaQ Solution#

The authors propose StaQ, a PMD variant for discrete action spaces that retains only the last $M$ Q-functions in memory rather than an infinite history. Their theoretical analysis demonstrates a key finding: when $M$ is large enough, this finite-memory approach delivers accurate policy updates without the errors inherent to existing approximations, while still preserving PMD's advantage of smoothing out policy evaluation mistakes.

Validation on Benchmark Tasks#

Using an optimized GPU implementation, the team tested StaQ on medium-scale RL benchmarks, particularly MinAtar. Their results show that increasing $M$ enhances performance up to a saturation point, beyond which gains level off and approach the performance of exact PMD. This empirical pattern aligns with the theoretical prediction that maintaining all historical Q-functions may be unnecessary in practice.

The work suggests that practitioners can achieve theoretically grounded performance improvements by simply keeping the most recent collection of Q-function estimates, offering a practical middle ground between computational efficiency and algorithmic soundness.