Integer programming lies at the heart of crucial combinatorial optimization tasks but remains challenging due to its NP-hard nature. An effective approach for practically solving integer programs is the manual design of acceleration cuts, i.e. inequalities that improve solver performance. However, this creative process demands deep expertise and is yet to be automated. Our proposed framework, EvoCut, automates the generation of acceleration cuts by combining large language models (LLMs) with an evolutionary search. EvoCut (i) initializes a diverse population of candidate cuts via an LLM-based initializer agent; (ii) for each cut empirically evaluates both preservation of the optimal solution and its ability to cut off fractional solutions across a verification set; and (iii) iteratively refines the population through evolutionary crossover and mutation agents. We quantify each cut's utility by its relative reduction in the solver's optimality gap. Our comparisons against standard integer programming practice show that EvoCut reduces optimality gap by 17-57% within a fixed time. It obtains the same solutions up to 4 times as fast, and obtains higher-quality solutions within the same time limit. Requiring no human expert input, EvoCut reliably generates, improves, and empirically verifies cuts that generalize to unseen instances. The code is available at https://github.com/milad1378yz/EvoCut.

Recent advances in diffusion models have shown remarkable potential for antibody design, yet existing approaches apply uniform generation strategies that cannot adapt to each antigen's unique requirements. Inspired by B cell affinity maturation--where antibodies evolve through multi-objective optimization balancing affinity, stability, and self-avoidance--we propose the first biologically-motivated framework that leverages physics-based domain knowledge within an online meta-learning system. Our method employs multiple specialized experts (van der Waals, molecular recognition, energy balance, and interface geometry) whose parameters evolve during generation based on iterative feedback, mimicking natural antibody refinement cycles. Instead of fixed protocols, this adaptive guidance discovers personalized optimization strategies for each target. Our experiments demonstrate that this approach: (1) discovers optimal SE(3)-equivariant guidance strategies for different antigen classes without pre-training, preserving molecular symmetries throughout optimization; (2) significantly enhances hotspot coverage and interface quality through target-specific adaptation, achieving balanced multi-objective optimization characteristic of therapeutic antibodies; (3) establishes a paradigm for iterative refinement where each antibody-antigen system learns its unique optimization profile through online evaluation; (4) generalizes effectively across diverse design challenges, from small epitopes to large protein interfaces, enabling precision-focused campaigns for individual targets.

Building capable household and industrial robots requires mastering the control of versatile, high-degree-of-freedom (DoF) systems such as mobile manipulators. While reinforcement learning (RL) holds promise for autonomously acquiring robot control policies, scaling it to high-DoF embodiments remains challenging. Direct RL in the real world demands both safe exploration and high sample efficiency, which are difficult to achieve in practice. Sim-to-real RL, on the other hand, is often brittle due to the reality gap. This paper introduces SLAC, a method that renders real-world RL feasible for complex embodiments by leveraging a low-fidelity simulator to pretrain a task-agnostic latent action space. SLAC trains this latent action space via a customized unsupervised skill discovery method designed to promote temporal abstraction, disentanglement, and safety, thereby facilitating efficient downstream learning. Once a latent action space is learned, SLAC uses it as the action interface for a novel off-policy RL algorithm to autonomously learn downstream tasks through real-world interactions. We evaluate SLAC against existing methods on a suite of bimanual mobile manipulation tasks, where it achieves state-of-the-art performance. Notably, SLAC learns contact-rich whole-body tasks in under an hour of real-world interactions, without relying on any demonstrations or hand-crafted behavior priors. More information and robot videos at robo-rl.github.io

Learning bimanual manipulation is challenging due to its high dimensionality and tight coordination required between two arms. Eye-in-hand imitation learning, which uses wrist-mounted cameras, simplifies perception by focusing on task-relevant views. However, collecting diverse demonstrations remains costly, motivating the need for scalable data augmentation. While prior work has explored visual augmentation in single-arm settings, extending these approaches to bimanual manipulation requires generating viewpoint-consistent observations across both arms and producing corresponding action labels that are both valid and feasible. In this work, we propose Diffusion for COordinated Dual-arm Data Augmentation (D-CODA), a method for offline data augmentation tailored to eye-in-hand bimanual imitation learning that trains a diffusion model to synthesize novel, viewpoint-consistent wrist-camera images for both arms while simultaneously generating joint-space action labels. It employs constrained optimization to ensure that augmented states involving gripper-to-object contacts adhere to constraints suitable for bimanual coordination. We evaluate D-CODA on 5 simulated and 3 real-world tasks. Our results across 2250 simulation trials and 300 real-world trials demonstrate that it outperforms baselines and ablations, showing its potential for scalable data augmentation in eye-in-hand bimanual manipulation. Our project website is at: https://dcodaaug.github.io/D-CODA/.

Hence, (14) holds following (11). Hence the KKT condition holds. Obviously, the condition that max( (), kr f () k, 1 / kr g () k) < + 1 can be replaced by a finite bound of the right hand side of (22), which is a weaker condition. Eq. (25) shows that R Assume f, g, r g, are continuously differentiable. In the lexico case, we have () 0 .

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems.

This motivates the following question: When does the Burer-Monteiro method converge to a globally optimal solution? This question has attracted much recent interest on the theoretical front.