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Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning~(RL),…

Reinforcement learning (RL) systems have countless applications, from energy-grid management to protein design. However, such real-world scenarios are often extremely difficult, combinatorial in nature, and require complex coordination…

Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…

We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee…

Mathematical reasoning tasks have become prominent benchmarks for assessing the reasoning capabilities of LLMs, especially with reinforcement learning (RL) methods such as GRPO showing significant performance gains. However, accuracy…

Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…

Reinforcement learning from human feedback (RLHF) aligns large language models (LLMs) by encouraging their generations to have high rewards, using a reward model trained on human preferences. To prevent the forgetting of pre-trained…

Direct Preference Optimization (DPO) has become a prominent method for aligning Large Language Models (LLMs) with human preferences. While DPO has enabled significant progress in aligning English LLMs, multilingual preference alignment is…

Reinforcement Learning with Verifiable Rewards (RLVR) has achieved substantial gains in single-attempt accuracy (Pass@1) on reasoning tasks, yet often suffers from reduced multi-sample coverage (Pass@K), indicating diversity collapse. We…

Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…

The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…

Reinforcement Learning with Verifiable Reward (RLVR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due…

Although outcome-based reinforcement learning (RL) significantly advances the mathematical reasoning capabilities of Large Language Models (LLMs), its reliance on computationally expensive ground-truth annotations imposes a severe…

Reward hacking is a form of misalignment in which models overoptimize proxy rewards without genuinely solving the underlying task. Precisely measuring reward hacking occurrence remains challenging because true task rewards are often…

We study the interpolation power of deep ReLU neural networks. Specifically, we consider the question of how efficiently, in terms of the number of parameters, deep ReLU networks can interpolate values at $N$ datapoints in the unit ball…

We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple…

Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex…

As the operations of autonomous systems generally affect simultaneously several users, it is crucial that their designs account for fairness considerations. In contrast to standard (deep) reinforcement learning (RL), we investigate the…

The versatility of recent machine learning approaches makes them ideal for improvement of next generation video compression solutions. Unfortunately, these approaches typically bring significant increases in computational complexity and are…

Dense process rewards have proven a more effective alternative to the sparse outcome-level rewards in the inference-time scaling of large language models (LLMs), particularly in tasks requiring complex multi-step reasoning. While dense…