Beyond variance reduction: Understanding the true impact of baselines on policy optimization
This work addresses a foundational issue in RL theory for researchers, revealing limitations in standard optimization frameworks, though it is incremental in extending analysis from bandits to MDPs.
The paper tackles the problem of understanding learning dynamics in bandit and reinforcement learning optimization, showing that traditional stochastic optimization assumptions are insufficient and that baseline choices critically affect convergence, with empirical validation in multi-state MDPs.
Bandit and reinforcement learning (RL) problems can often be framed as optimization problems where the goal is to maximize average performance while having access only to stochastic estimates of the true gradient. Traditionally, stochastic optimization theory predicts that learning dynamics are governed by the curvature of the loss function and the noise of the gradient estimates. In this paper we demonstrate that this is not the case for bandit and RL problems. To allow our analysis to be interpreted in light of multi-step MDPs, we focus on techniques derived from stochastic optimization principles (e.g., natural policy gradient and EXP3) and we show that some standard assumptions from optimization theory are violated in these problems. We present theoretical results showing that, at least for bandit problems, curvature and noise are not sufficient to explain the learning dynamics and that seemingly innocuous choices like the baseline can determine whether an algorithm converges. These theoretical findings match our empirical evaluation, which we extend to multi-state MDPs.