We propose two simple, principled and practical algorithms that enjoy provable scaling laws for the test-time compute of large language models (LLMs). The first one is a two-stage knockout-style algorithm: given an input problem, it first generates multiple candidate solutions, and then aggregate them via a knockout tournament for the final output. Assuming that the LLM can generate a correct solution with non-zero probability and do better than a random guess in comparing a pair of correct and incorrect solutions, we prove theoretically that the failure probability of this algorithm decays to zero exponentially or by a power law (depending on the specific way of scaling) as its test-time compute grows. The second one is a two-stage league-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents, rather than eliminated upon loss to a single opponent. Under analogous but more robust assumptions, we prove that its failure probability also decays to zero exponentially with more test-time compute. Both algorithms require a black-box LLM and nothing else (e.g., no verifier or reward model) for a minimalistic implementation, which makes them appealing for practical applications and easy to adapt for different tasks. Through extensive experiments with diverse models and datasets, we validate the proposed theories and demonstrate the outstanding scaling properties of both algorithms.

Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning, i.e., optimization with a decision maker in the loop, allows us to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are typically monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and allows learning the decision maker's preferences from pairwise comparisons. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and is robust to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.

We study the problem of aligning a generative model's response with a user's preferences. Recent works have proposed several different formulations for personalized alignment; however, they either require a large amount of user preference queries or require that the preference be explicitly specified as a text input. In this paper, we propose a novel inference-time personalized alignment method, USERALIGN, that elicits the user's preferences with a few queries as pairwise response comparisons. In particular, USERALIGN builds on the theoretical framework of best-arm identification in logistic bandits and selects a personalized response from a fixed pool of the model's generated responses. The key idea is to consider the user's feedback consistent and noise-free, and incorporate it into the theoretical framework to identify the best response quickly.

After pre-training, large language models are aligned with human preferences based on pairwise comparisons. State-of-the-art alignment methods (such as PPO-based RLHF and DPO) are built on the assumption of aligning with a single preference model, despite being deployed in settings where users have diverse preferences. As a result, it is not even clear that these alignment methods produce models that satisfy users on average -- a minimal requirement for pluralistic alignment. Drawing on social choice theory and modeling users' comparisons through individual BradleyTerry (BT) models, we introduce an alignment method's distortion: the worst-case ratio between the optimal achievable average utility, and the average utility of the learned policy. The notion of distortion helps draw sharp distinctions between alignment methods: Nash Learning from Human Feedback achieves the minimax optimal distortion of (12+o(1)) β (for the BT temperature β), robustly across utility distributions, distributions of comparison pairs, and permissible KL divergences from the reference policy. RLHF and DPO, by contrast, suffer (1 o(1)) β distortion already without a KL constraint, and eΩ(β) or even unbounded distortion in the full setting, depending on how comparison pairs are sampled.

The advent of large language models (LLMs) offers unprecedented opportunities to reimagine peer review beyond the constraints of traditional workflows. Despite these opportunities, prior efforts have largely focused on replicating traditional review workflows with LLMs serving as direct substitutes for human reviewers, while limited attention has been given to exploring new paradigms that fundamentally rethink how LLMs can participate in the academic review process. In this paper, we introduce and explore a novel mechanism that employs LLM agents to perform pairwise comparisons among manuscripts instead of individual scoring. By aggregating outcomes from substantial pairwise evaluations, this approach enables a more accurate and robust measure of relative manuscript quality. Our experiments demonstrate that this comparative approach significantly outperforms traditional rating-based methods in identifying high-impact papers. However, our analysis also reveals emergent biases in the selection process, notably a reduced novelty in research topics and an increased institutional imbalance. These findings highlight both the transformative potential of rethinking peer review with LLMs and critical challenges that future systems must address to ensure equity and diversity.

Bayesian optimization (BO) is a popular and effective approach for tuning expensive, noisy experiments, but requires the formulation of an explicit objective function. Preferential BO (PBO) removes this requirement by learning from pairwise human feedback, yet existing methods struggle to efficiently optimize beyond low- and medium-dimensional problems due to their global search approaches. We address this limitation by developing a family of local PBO methods that transfer key ideas from high-dimensional BO to the preferential setting. In particular, we introduce local PBO methods which adapt trust-region and derivative-informed local search to pairwise preference feedback, where the latter exploits first- and second-order derivatives of the Laplace-approximated GP posterior. Our benchmark on GP sample paths, standard optimization benchmark functions, and policy-search tasks shows that local PBO methods are especially effective in high-dimensional and complex landscapes with steep optima. Compared with global preference-based baselines, they can substantially reduce cumulative regret, making them particularly useful for real-world preference-based optimization tasks such as policy search.

We study the sample complexity (i.e., the number of comparisons needed) bounds for actively ranking a set of n items from multi-wise comparisons. Here, a multiwise comparison takes m items as input and returns a (noisy) result about the best item (the winner feedback) or the order of these items (the full-ranking feedback). We consider two basic ranking problems: top-k items selection and full ranking. Unlike previous works that study ranking from multi-wise comparisons, in this paper, we do not require any parametric model or assumption and work on the fundamental setting where each comparison returns the correct result with probability 1or a certain probability larger than 12. This paper helps understand whether and to what degree utilizing multi-wise comparisons can reduce the sample complexity for the ranking problems compared to ranking from pairwise comparisons. Specifically, under the winner feedback setting, one can reduce the sample complexity for top-k selection up to an m factor and that for full ranking up to a logm factor. Under the full-ranking feedback setting, one can reduce the sample complexity for top-k selection up to an m factor and that for full ranking up to an mlogm factor. We also conduct numerical simulations to confirm our theoretical results.

Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect to be corrected immediately. In this article, we adopt a different point of view: part of the nonreciprocity may reflect a genuine variation in the evaluation scale, while another part is due to random perturbations. We introduce an additive model in which the unknown underlying comparison matrix is consistent but not necessarily reciprocal. The reciprocal component carries the global ranking information, whereas the symmetric component describes possible scale variation. Around this structured matrix, we add a random perturbation and show how to estimate the noise level, assess whether the scale variation remains moderate, and assign probabilities to admissible ranking regions in the sense of strict ranking by pairwise comparisons. We also compare this approach with the brutal projection onto reciprocal matrices, which suppresses all symmetric information at once. The Gaussian perturbation model is used here not because human decisions are exactly Gaussian, but because observed judgment errors often result from the accumulation of many small effects. In such a context, the central limit principle provides a natural heuristic justification for Gaussian noise. This makes it possible to derive explicit estimators and probability assessments while keeping the model interpretable for decision problems.