Existing procedures seek configurations that minimize expected runtime.

Contract theory studies the setting where a principal seeks to design a contract for rewarding an agent on the basis of the uncertain outcomes caused by the agent's private actions [

We summarize our contributions as follows: 1.

Wang et al. [ 2022 ] considered an online resource allocation problem where the

Suppose a revenue-maximizing recommendation algorithm concludes from past data that more revenue is generated by showing the ad to Group A compared to Group B. In that case, the ad-serving algorithm will eventually end up showing that ad exclusively to Group A

We study the multinomial logit (MNL) contextual bandit problem for sequential assortment selection. Although most existing research assumes utility functions to be linear in item features, this linearity assumption restricts the modeling of intricate interactions between items and user preferences. A recent work (Zhang & Luo, 2024) has investigated general utility function classes, yet its method faces fundamental trade-offs between computational tractability and statistical efficiency. To address this limitation, we propose a computationally efficient algorithm for MNL contextual bandits leveraging the upper confidence bound principle, specifically designed for non-linear parametric utility functions, including those modeled by neural networks. Under a realizability assumption and a mild geometric condition on the utility function class, our algorithm achieves a regret bound of $\tilde{O}(\sqrt{T})$, where $T$ denotes the total number of rounds. Our result establishes that sharp $\tilde{O}(\sqrt{T})$-regret is attainable even with neural network-based utilities, without relying on strong assumptions such as neural tangent kernel approximations. To the best of our knowledge, our proposed method is the first computationally tractable algorithm for MNL contextual bandits with non-linear utilities that provably attains $\tilde{O}(\sqrt{T})$ regret. Comprehensive numerical experiments validate the effectiveness of our approach, showing robust performance not only in realizable settings but also in scenarios with model misspecification.

The critical challenge when using the Shapley value is its well-known computational intractability.

Multi-objective reinforcement learning (MORL) is an excellent framework for multi-objective sequential decision-making. MORL employs a utility function to aggregate multiple objectives into one that expresses a user's preferences. However, MORL still misses two crucial theoretical analyses of the properties of utility functions: (1) a characterisation of the utility functions for which an associated optimal policy exists, and (2) a characterisation of the types of preferences that can be expressed as utility functions. As a result, we formally characterise the families of preferences and utility functions that MORL should focus on: those for which an optimal policy is guaranteed to exist. We expect our theoretical results to promote the development of novel MORL algorithms that exploit our theoretical findings.