Research

Abstract : How should a decision-maker sequentially allocate treatments when treatment effects vary with observed covariates and are small relative to sampling noise? We study this contextual bandit problem under root-n local asymptotics. At each decision node, the decision-maker uses past observations to select a covariate-dependent allocation rule. We show that the optimal Bayes regret over all measurable adaptive policy converges to the value of a limiting gaussian belief-state dynamic program. A finite-sample analogue of an optimal policy for this limiting problem is asymptotically optimal.

We then allow for an unknown additive component to all treatment arms, as arises naturally in linear contextual bandits. Although this baseline cancels from treatment comparisons, it affects the distribution of observations used to guide future allocations. We consider a criterion that averages over a prior on local treatment effects and takes the worst case over the additive shift. We construct a limiting dynamic program whose value equals the asymptotic value of this criterion and show that it admits an optimal policy invariant to additive shifts. A finite-sample analogue of this policy attains the asymptotic optimum.

Abstract : We study dynamic pricing for public goods using a weighted objective that balances seller revenue and consumer surplus. We formulate the problem within a Bayesian online learning framework where the underlying demand function is unknown and is assigned a prior distribution. We demonstrate that standard Thompson Sampling can fail in this setting, potentially incurring linear regret. To address this, we propose using Information-Directed Sampling (IDS). We prove that IDS achieves the Bayesian regret rate matching known lower bounds up to a poly-logarithmic factor.