Saturation-Insensitive Dueling Bandits with General Function Approximation

Contextual dueling bandits learn from pairwise comparisons, the same feedback used to fine-tune language models from human preferences. Standard algorithms explore aggressively and can show users two poor options. We study conservative contextual dueling bandits, which require that, at every round, the cumulative score of the better displayed item stay above a $(1-α)$ fraction of a trusted baseline's. An item's score is its probability of beating the best available item, so the constraint depends only on utility differences and needs no absolute rewards. This also changes how safety can be certified: we show that transferring the safety test of the conservative bandit algorithm CLUCB unchanged can incur linear regret, even when the baseline's utilities are known exactly. For linear utilities, we develop MaxInP-BC, which certifies scores through utility gaps and, when it must fall back, pairs the baseline with an informative partner so that fallback rounds still drive learning. It is safe with high probability at all times, with regret $\tilde{O}(d\sqrt{T}/κ)$ plus an additive cost of conservatism that does not grow with the horizon. For general utility classes, we develop BTIGW-BC, which turns the guarantee of an online logistic-regression oracle into cumulative safety certificates. It is safe at all times, makes finitely many fallbacks, and has sublinear regret whenever the oracle's logistic regret is sublinear. In experiments, both satisfy the constraint, which their unconstrained counterparts often violate, at a moderate cost in regret.

Contextual dueling bandits form a cornerstone of preference-based decision-making, with critical applications in recommender systems and large language model alignment. However, standard algorithms rely on the idealized assumption of immediate feedback, a condition frequently violated in real-world scenarios such as prompt optimization. This setting introduces a unique theoretical challenge: unlike linear bandits, dueling bandit estimators lack closed-form solutions, rendering naive adaptations of standard weighting techniques biased. To address this, we formalize the problem of Contextual Dueling Bandits with Stochastic Delayed Feedback and propose two novel algorithms: Linear (LDB-DF) and Neural (NDB-DF) Dueling Bandits with Delayed Feedback. Central to our approach is a novel estimator that integrates an Inverse Probability Weighting (IPW) mechanism directly into the loss function, ensuring unbiased correction for delayed or missing feedback. We provide comprehensive theoretical analysis, establishing an O(d*sqrt(T)) regret bound for the linear setting and sub-linear guarantees for the neural setting. Extensive experiments on both simulated and real-world datasets demonstrate the effectiveness of our propose.

Dueling bandits choose each comparison based on earlier noisy outcomes, so two runs on the same preferences can compare different pairs. We study replicable dueling bandits, where two executions with shared internal randomness and independent comparison outcomes must select the same ordered pair in every round with probability at least $1-ρ$. Building on Beat-the-Mean, whose scores change as arms are eliminated and need not rank the best arm highest, we design the first such algorithms with sublinear regret. Under relaxed stochastic transitivity with parameter $γ\ge 1$ and the stochastic triangle inequality, we design an algorithm that achieves expected regret $\widetilde{O}(γ^8 K^4 H_{\mathrm{p}}/ρ^2)$, where $H_{\mathrm{p}}=\sum_{i=2}^{K}(P_{1i}-1/2)^{-1}$. Under strong stochastic transitivity, we design an algorithm based on simultaneous elimination that improves the dependence on $K$ and achieves $\widetilde{O}(K^2 H_{\mathrm{p}}/ρ^2)$ regret. For linear dueling bandits, we design an algorithm that achieves regret $\widetilde{O}(d^3\sqrt{T}/(c_μρ))$. Experiments on synthetic and language-model preferences show replicability, with sublinear regret.