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Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and significantly impacts industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary…
Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…
The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of…
Oversampling is one of the most widely used approaches for addressing imbalanced classification. The core idea is to generate additional minority samples to rebalance the dataset. Most existing methods, such as SMOTE, require converting…
Classical optimization algorithms--hill climbing, simulated annealing, population-based methods--generate candidate solutions via random perturbations. We replace the random proposal generator with an LLM agent that reasons about evaluation…
Latent variables pose a fundamental challenge to causal discovery and inference. Conventional local methods focus on direct neighbors but fail to provide macro level insights. Cluster level methods enable macro causal reasoning but either…
Decoding from large language models (LLMs) typically relies on fixed sampling hyperparameters (e.g., temperature, top-p), despite substantial variation in task difficulty and uncertainty across prompts and individual decoding steps. We…
In latent Dirichlet allocation (LDA), topics are multinomial distributions over the entire vocabulary. However, the vocabulary usually contains many words that are not relevant in forming the topics. We adopt a variable selection method…
We consider the setting of online convex optimization with adversarial time-varying constraints in which actions must be feasible w.r.t. a fixed constraint set, and are also required on average to approximately satisfy additional…
A Low-rank Spectral Optimization Problem (LSOP) minimizes a linear objective subject to multiple two-sided linear matrix inequalities intersected with a low-rank and spectral constrained domain set. Although solving LSOP is, in general,…
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…
We initiate the mathematical study of replicability as an algorithmic property in the context of reinforcement learning (RL). We focus on the fundamental setting of discounted tabular MDPs with access to a generative model. Inspired by…
Listwise reranking utilizing Large Language Models (LLMs) has achieved state-of-the-art retrieval effectiveness. Recently, reasoning-enhanced models have further pushed these boundaries by employing Chain-of-Thought (CoT) to perform deep…
Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query…
Most offline reinforcement learning (RL) algorithms return a target policy maximizing a trade-off between (1) the expected performance gain over the behavior policy that collected the dataset, and (2) the risk stemming from the…
We study an online linear programming (OLP) problem under a random input model in which the columns of the constraint matrix along with the corresponding coefficients in the objective function are generated i.i.d. from an unknown…
Structural pruning techniques are essential for deploying multimodal large language models (MLLMs) across various hardware platforms, from edge devices to cloud servers. However, current pruning methods typically determine optimal…
Local search algorithms applied to optimization problems often suffer from getting trapped in a local optimum. The common solution for this deficiency is to restart the algorithm when no progress is observed. Alternatively, one can start…
Effective exploration is a key challenge in reinforcement learning for large language models: discovering high-quality trajectories within a limited sampling budget from the vast natural language sequence space. Existing methods face…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…