In this paper we consider the dynamic assortment selection problem under an uncapacitated multinomial-logit (MNL) model. By carefully analyzing a revenue potential function, we show that a trisection based algorithm achieves an item-independent regret bound of Op? T log log T q, which matches information theoretical lower bounds up to iterated logarithmic terms. Our proof technique draws tools from the unimodal/convex bandit literature as well as adaptive confidence parameters in minimax multi-armed bandit problems.

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There has been much interest in recent years in the problem of dueling bandits, where on each round the learner plays a pair of arms and receives as feedback the outcome of a relative pairwise comparison between them.

We consider a preference learning setting where every participant chooses an ordered listofkmost preferred items among adisplayed setofcandidates.

Determining the subset (or assortment) of items to offer is a key decision problem that commonly arises in several application contexts.

Alignment of large language models (LLMs) has predominantly relied on pairwise preference optimization, where annotators select the better of two responses to a prompt. While simple, this approach overlooks the opportunity to learn from richer forms of human feedback, such as multiwise comparisons and top-$k$ rankings. We propose Ranked Choice Preference Optimization (RCPO), a unified framework that bridges preference optimization with (ranked) choice modeling via maximum likelihood estimation. The framework is flexible, supporting both utility-based and rank-based choice models. It subsumes several existing pairwise methods (e.g., DPO, SimPO), while providing principled training objectives for richer feedback formats. We instantiate this framework with two representative ranked choice models (Multinomial Logit and Mallows-RMJ). Empirical studies on Llama-3-8B-Instruct and Gemma-2-9B-it across AlpacaEval 2 and Arena-Hard benchmarks show that RCPO consistently outperforms competitive baselines. RCPO shows how directly leveraging ranked preference data, combined with the right choice models, yields more effective alignment. It offers a versatile and extensible foundation for incorporating (ranked) choice modeling into LLM training.

We extend the multinomial logit model to represent some of the empirical phenomena that are frequently observed in the choices made by humans. These phenomena include the similarity effect, the attraction effect, and the compromise effect. We formally quantify the strength of these phenomena that can be represented by our choice model, which illuminates the flexibility of our choice model. We then show that our choice model can be represented as a restricted Boltzmann machine and that its parameters can be learned effectively from data. Our numerical experiments with real data of human choices suggest that we can train our choice model in such a way that it represents the typical phenomena of choice.