Learning Good Interventions in Causal Contextual Bandits with Adaptive Context

Rahul Madhavan, Gaurav Sinha, Aurghya Maiti, Siddharth Barman

Primary Area: causal reasoning

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Keywords: Causal Bandits, Causality, Causal Inference, Simple Regret, Contextual Bandits, Causal Contextual Bandits, Convex Exploration, Intervention Complexity, Simple Regret, Simple regret lower bound

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TL;DR: We propose a near-optimal algorithm for simple regret in causal contextual bandits where the context is stochastically dependent on an initial action chosen by the learner.

Abstract: We study a variant of causal contextual bandits where the context is stochastically dependent on an initial action chosen by the learner. This adaptive context setting allows the environment to elicit some initial choice from the learner before providing the context. Upon observing the context, the learner picks another action (an intervention in a causal graph) based on which they receive a reward. The objective is to identify near-optimal atomic causal interventions at the initial state and post context identification, to maximize reward. We extend prior work from the deterministic context setting to obtain simple regret minimization guarantees. This is achieved through an instance-dependent causal parameter, $\lambda$, which characterizes our upper bound. Furthermore, we prove that our simple regret is essentially tight for a large class of instances. A key feature of our work is that we use convex optimization to address the bandit exploration problem. We also conduct experiments to validate our theoretical results

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Submission Number: 5332