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The Importance of Pessimism in Fixed-Dataset Policy Optimization

Jacob Buckman, Carles Gelada, Marc G. Bellemare

TL;DR

This work addresses the problem of learning high-return policies from fixed datasets (FDPO) by establishing worst-case guarantees. It introduces the pessimism principle, analyzes naïve versus pessimistic strategies, and derives two principled families of pessimistic FDPO algorithms: uncertainty-aware and proximal. The authors prove suboptimality bounds that show pessimism can yield strong performance even when the dataset does not fully inform every policy, and they validate the theory with gridworld and MinAtar experiments. The results have practical implications for RL, highlighting the potential of uncertainty-aware methods to improve sample efficiency and reliability when learning from fixed data.

Abstract

We study worst-case guarantees on the expected return of fixed-dataset policy optimization algorithms. Our core contribution is a unified conceptual and mathematical framework for the study of algorithms in this regime. This analysis reveals that for naive approaches, the possibility of erroneous value overestimation leads to a difficult-to-satisfy requirement: in order to guarantee that we select a policy which is near-optimal, we may need the dataset to be informative of the value of every policy. To avoid this, algorithms can follow the pessimism principle, which states that we should choose the policy which acts optimally in the worst possible world. We show why pessimistic algorithms can achieve good performance even when the dataset is not informative of every policy, and derive families of algorithms which follow this principle. These theoretical findings are validated by experiments on a tabular gridworld, and deep learning experiments on four MinAtar environments.

The Importance of Pessimism in Fixed-Dataset Policy Optimization

TL;DR

This work addresses the problem of learning high-return policies from fixed datasets (FDPO) by establishing worst-case guarantees. It introduces the pessimism principle, analyzes naïve versus pessimistic strategies, and derives two principled families of pessimistic FDPO algorithms: uncertainty-aware and proximal. The authors prove suboptimality bounds that show pessimism can yield strong performance even when the dataset does not fully inform every policy, and they validate the theory with gridworld and MinAtar experiments. The results have practical implications for RL, highlighting the potential of uncertainty-aware methods to improve sample efficiency and reliability when learning from fixed data.

Abstract

We study worst-case guarantees on the expected return of fixed-dataset policy optimization algorithms. Our core contribution is a unified conceptual and mathematical framework for the study of algorithms in this regime. This analysis reveals that for naive approaches, the possibility of erroneous value overestimation leads to a difficult-to-satisfy requirement: in order to guarantee that we select a policy which is near-optimal, we may need the dataset to be informative of the value of every policy. To avoid this, algorithms can follow the pessimism principle, which states that we should choose the policy which acts optimally in the worst possible world. We show why pessimistic algorithms can achieve good performance even when the dataset is not informative of every policy, and derive families of algorithms which follow this principle. These theoretical findings are validated by experiments on a tabular gridworld, and deep learning experiments on four MinAtar environments.

Paper Structure

This paper contains 59 sections, 12 theorems, 60 equations, 3 figures, 8 algorithms.

Table of Contents

  1. Introduction
  2. How Proxy Objectives Impact Regret
  3. FDPO Background
  4. Naïve Algorithms
  5. The Pessimism Principle
  6. Uncertainty-Aware Pessimistic Algorithms
  7. Proximal Pessimistic Algorithms
  8. The Relationship Between Uncertainty-Aware and Proximal Algorithms
  9. Experiments
  10. Tabular.
  11. Neural network.
  12. Discussion and Conclusion
  13. Future directions.
  14. On ad-hoc solutions.
  15. Stochastic policies.
  16. ...and 44 more sections

Key Result

Theorem 1

For any space $\mathcal{X}$, objective $f : \mathcal{X} \to \mathbb{R}$, and proxy objective $\hat{f} : \mathcal{X} \to \mathbb{R}$, where $x^* := \mathop{\mathrm{arg\,max}}\limits_{x \in \mathcal{X}} f(x)$ and $\hat{x}^* := \mathop{\mathrm{arg\,max}}\limits_{x \in \mathcal{X}} \hat{f}(x)$. Furthermore, this bound is tight.

Figures (3)

  • Figure 1: Tabular gridworld experiments.
  • Figure 2: Performance of deep FDPO algorithms on a dataset of 500000 transitions, as the data collection policy is interpolated from near-optimal to random.
  • Figure 3: Bandit-like MDP, with accompanying dataset. $\mu$ gives the true mean of each action. $n$D gives the counts of the pulls used to construct dataset $D$, and $\mu$D gives our empirical estimate of the mean reward. On this problem, any algorithm that selects the action with the highest empirical mean reward will almost always pick a suboptimal action. In contrast, a pessimistic algorithm, which selects the action with the highest lower bound, will almost always pick the correct action.

Theorems & Definitions (30)

  • Theorem 1
  • proof
  • Corollary 1: Value-based FDPO suboptimality bound
  • Definition 1
  • Theorem 2: Naïve FDPO suboptimality bound
  • proof
  • Definition 2
  • Theorem 3: Uncertainty-aware pessimistic FDPO suboptimality bound
  • proof
  • Definition 3
  • ...and 20 more