Conversational Generalized Linear Bandits with Hybrid Feedback

We study fixed-confidence best arm identification in generalized linear bandits under a hybrid feedback model: at each round, the learner may query either (i) absolute reward feedback from a single arm or (ii) relative (dueling) feedback from an arm pair, both governed by generalized linear models. We introduce a likelihood-ratio--based confidence sequence that unifies heterogeneous generalized linear observations and yields an explicit ellipsoidal confidence set under a self-concordance assumption. Building on this confidence set, we propose a hybrid Track-and-Stop algorithm that adaptively allocates queries by tracking a minimax-optimal design over a joint action space of arms and pairs. We establish $δ$-correctness and provide high-probability upper bounds on the stopping time. We further extend the framework to a cost-aware setting that accounts for heterogeneous acquisition costs across feedback modalities. Empirical experiments demonstrate that the proposed algorithms significantly improve sample efficiency over baseline methods.

Personalized decision-making in multi-objective bandits requires learning user-specific trade-offs among competing objectives. Since arm utility depends on both unknown rewards and unknown preferences, existing methods infer preferences only from utility feedback, entangling preference learning with reward exploration. In practice, however, users often reveal their priorities through proactive conversational queries (e.g., "cheap and clean hotel"), yet this structured signal is not leveraged. We formalize a proactive query-based framework in which user queries provide structured preference signals. Modeling these signals via a Plackett-Luce subset choice model, we show that query-only learning is insufficient due to a fundamental shift-invariance barrier. To resolve this, we introduce MO-PQUCB, a hybrid algorithm that integrates query-based preference anchoring with bandit feedback through shift-invariant regularization and dual-exploration UCB. We prove that proactive queries accelerate preference estimation and yield improved regret scaling over prior preference-aware MO-MAB methods. Under corrupted queries, we further characterize statistical limits and design a robust estimator achieving near-optimal performance when the corruption is sparse. Experiments validate both theoretical and practical gains.

We study preference-based bandits with general reward function classes, where a learner sequentially selects pairs of arms and observes binary preference feedback governed by the Bradley--Terry model. This setting naturally arises in applications such as recommender systems, tournament ranking, and learning from human feedback, where relative preferences are easier to elicit than absolute rewards. The observation model inherits the logistic bandit challenge of handling the problem-dependent constant $κ$, which accounts for the non-linearity of the link function and can grow arbitrarily large. Moreover, prior work has predominantly focused on linear or kernelized reward models, precluding the use of richer function classes. To address these limitations, we consider general reward function classes and introduce the locally sensitive eluder dimension, a novel complexity measure tailored to the logistic structure of preference feedback that yields fine-grained regret guarantees without unfavorable dependence on $κ$. Building on this notion, we propose GINOP (Generic INformative OPtimism), an algorithm that constructs log-loss confidence sets and jointly selects arm pairs to balance optimism and informative exploration. We establish a first-order regret bound that, in contrast with what previous results suggest, demonstrates that learning with preference feedback is as statistically efficient as learning from direct reward observation. Finally, we corroborate our theoretical findings with empirical evaluations against competitive baselines.