Instance-Dependent Complexity of Contextual Bandits and Reinforcement Learning: A Disagreement-Based Perspective (2010.03104v1)

Abstract: In the classical multi-armed bandit problem, instance-dependent algorithms attain improved performance on "easy" problems with a gap between the best and second-best arm. Are similar guarantees possible for contextual bandits? While positive results are known for certain special cases, there is no general theory characterizing when and how instance-dependent regret bounds for contextual bandits can be achieved for rich, general classes of policies. We introduce a family of complexity measures that are both sufficient and necessary to obtain instance-dependent regret bounds. We then introduce new oracle-efficient algorithms which adapt to the gap whenever possible, while also attaining the minimax rate in the worst case. Finally, we provide structural results that tie together a number of complexity measures previously proposed throughout contextual bandits, reinforcement learning, and active learning and elucidate their role in determining the optimal instance-dependent regret. In a large-scale empirical evaluation, we find that our approach often gives superior results for challenging exploration problems. Turning our focus to reinforcement learning with function approximation, we develop new oracle-efficient algorithms for reinforcement learning with rich observations that obtain optimal gap-dependent sample complexity.

Instance-Dependent Complexity of Contextual Bandits and Reinforcement Learning

The paper of contextual bandits and reinforcement learning has been pivotal in advancing adaptive decision-making processes, where systems learn to make decisions based on contextual information. This paper explores the intricate details of instance-dependent complexity within these domains, offering new perspectives on how to achieve enhanced performance when operating in high-dimensional and rich context environments.

The classical multi-armed bandit problem, where players choose from several options to maximize rewards over time, serves as a foundational concept. In such setups, algorithms that incorporate instance-dependent algorithms—those that tailor their behavior based on the 'difficulty' or characteristics of the task—can significantly outperform generic algorithms. This performance boost is primarily noticeable for "easy" problems, where there is a clear distinction between the best and second-best actions. However, this paper extends the discussion to contextual bandits, where contexts dynamically influence decision-making.

Key Contributions

1. Complexity Measures for Contextual Bandits: A main thrust of the paper is in the introduction of new complexity measures necessary for grasping the nuances of instance-dependent regret bounds in contextual bandits. These measures provide a theoretical framework for understanding when and how such bounds can be achieved, filling an existing gap in literature for comprehensive theories that support general policy classes.
2. Oracle-Efficient Algorithms: The paper proposes oracle-efficient algorithms which aim to capitalize on identifiable gaps. These algorithms are designed to adjust and react to specific instances, achieving optimal performance with minimal regret across both 'easy' and 'hard' instances. The foundational algorithm presented in this research, AdaCB, exploits the potential of instance-dependent adaptations.
3. Reinforcement Learning with Function Approximation: The paper transitions its focus to reinforcement learning, specifically examining block MDPs—a complex decision-making environment modeled to reflect more realistic scenarios where states evolve based on past actions. It introduces scalable algorithms that encapsulate rich observations and integrate function approximation techniques, allowing for optimal sample complexity.
4. Empirical Findings: Extensive empirical evaluations are performed to demonstrate the superior efficacy of the proposed algorithms in challenging exploration scenarios, often surpassing existing state-of-the-art methods.

Theoretical Insights

The structural insights provided by this paper are profound; they challenge existing norms about the distributional assumptions necessary for achieving low-instance-dependent regret. The research ties various complexity measures previously considered disparate, linking them in a cohesive framework that accounts for optimal policy determination under variable conditions—whether in bandits or reinforcement-based environments.

Moreover, the paper underlines the importance of adaptability in learning algorithms, eschewing the one-size-fits-all approach in favor of algorithms that can self-adjust to the complexity and dynamics observed in the data.

Implications and Future Directions

From a theoretical standpoint, this work provides a foundational basis for examining contextual bandits and reinforcement learning through the lens of context-aware adaptations. Practically, the implications are vast for fields like healthcare, finance, and automated control systems, where decision-making is deeply rooted in contextual evaluation.

Future research may be directed towards extending these framework approaches to even more complex models of decision processes, potentially involving adversarial settings or those with continuous action spaces. Additionally, further exploration into refining the computational efficiency of these algorithms could unlock further applications and real-time processing capabilities.

Overall, this paper constitutes a noteworthy advance in the research of instance-dependent complexity in contextual bandits and reinforcement learning—an essential step forward for developing more adept decision-making systems in our increasingly data-driven world.