Contextual Bandit Learning with Predictable Rewards

TL;DR

This paper introduces a new algorithm for contextual bandit learning under a realizability assumption, achieving near-optimal regret bounds and demonstrating scenarios where it outperforms previous methods.

Contribution

The paper proposes Regressor Elimination, a novel algorithm with regret bounds comparable to the agnostic setting, and provides lower bounds and scenarios where it excels.

Findings

Regressor Elimination achieves regret similar to agnostic algorithms.

A new lower bound shows no algorithm can do better in the worst case.

The algorithm has constant regret for certain reward distributions.

Abstract

Contextual bandit learning is a reinforcement learning problem where the learner repeatedly receives a set of features (context), takes an action and receives a reward based on the action and context. We consider this problem under a realizability assumption: there exists a function in a (known) function class, always capable of predicting the expected reward, given the action and context. Under this assumption, we show three things. We present a new algorithm---Regressor Elimination--- with a regret similar to the agnostic setting (i.e. in the absence of realizability assumption). We prove a new lower bound showing no algorithm can achieve superior performance in the worst case even with the realizability assumption. However, we do show that for any set of policies (mapping contexts to actions), there is a distribution over rewards (given context) such that our new algorithm has constant regret unlike the previous approaches.