The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the component of interest, such as the location of the optimum. Nuisance parameters are eliminated via profile likelihood, which naturally handles constraints. As a direct instantiation, we develop a MINimalist Thompson Sampling (MINTS) algorithm. Our framework accommodates structured problems, including continuum-armed Lipschitz bandits and dynamic pricing. It also provides a probabilistic lens on classical convex optimization algorithms such as the center of gravity and ellipsoid methods. We further analyze MINTS for multi-armed bandits and establish near-optimal regret guarantees.

We introduce a comprehensive framework for the detection and demodulation of covert electromagnetic signals using solid-state spin sensors. Our approach, named RAPID, is a two-stage hybrid strategy that leverages nitrogen-vacancy (NV) centers to operate below the classical noise floor employing a robust adaptive policy via imitation and distillation. We first formulate the joint detection and estimation task as a unified stochastic optimal control problem, optimizing a composite Bayesian risk objective under realistic physical constraints. The RAPID algorithm solves this by first computing a robust, non-adaptive baseline protocol grounded in the quantum Fisher information matrix (QFIM), and then using this baseline to warm-start an online, adaptive policy learned via deep reinforcement learning (Soft Actor-Critic). This method dynamically optimizes control pulses, interrogation times, and measurement bases to maximize information gain while actively suppressing non-Markovian noise and decoherence. Numerical simulations demonstrate that the protocol achieves a significant sensitivity gain over static methods, maintains high estimation precision in correlated noise environments, and, when applied to sensor arrays, enables coherent quantum beamforming that achieves Heisenberg-like scaling in precision. This work establishes a theoretically rigorous and practically viable pathway for deploying quantum sensors in security-critical applications such as electronic warfare and covert surveillance.

We propose Delta Velocity Rectified Flow (DVRF), a novel inversion-free, path-aware editing framework within rectified flow models for text-to-image editing. DVRF is a distillation-based method that explicitly models the discrepancy between the source and target velocity fields in order to mitigate over-smoothing artifacts rampant in prior distillation sampling approaches. We further introduce a time-dependent shift term to push noisy latents closer to the target trajectory, enhancing the alignment with the target distribution. We theoretically demonstrate that when this shift is disabled, DVRF reduces to Delta Denoising Score, thereby bridging score-based diffusion optimization and velocity-based rectified-flow optimization. Moreover, when the shift term follows a linear schedule under rectified-flow dynamics, DVRF generalizes the Inversion-free method FlowEdit and provides a principled theoretical interpretation for it. Experimental results indicate that DVRF achieves superior editing quality, fidelity, and controllability while requiring no architectural modifications, making it efficient and broadly applicable to text-to-image editing tasks. Code is available at https://github.com/Harvard-AI-and-Robotics-Lab/DeltaVelocityRectifiedFlow.

We consider two-player zero-sum concurrent stochastic games (CSGs) played on graphs with reachability and safety objectives. These include degenerate classes such as Markov decision processes or turn-based stochastic games, which can be solved by linear or quadratic programming; however, in practice, value iteration (VI) outperforms the other approaches and is the most implemented method. Similarly, for CSGs, this practical performance makes VI an attractive alternative to the standard theoretical solution via the existential theory of reals. VI starts with an under-approximation of the sought values for each state and iteratively updates them, traditionally terminating once two consecutive approximations are $ε$-close. However, this stopping criterion lacks guarantees on the precision of the approximation, which is the goal of this work. We provide bounded (a.k.a. interval) VI for CSGs: it complements standard VI with a converging sequence of over-approximations and terminates once the over- and under-approximations are $ε$-close.

We study the linear convergence of Frank-Wolfe algorithms over product polytopes. We analyze two condition numbers for the product polytope, namely the \emph{pyramidal width} and the \emph{vertex-facet distance}, based on the condition numbers of individual polytope components. As a result, for convex objectives that are $μ$-Polyak-Łojasiewicz, we show linear convergence rates quantified in terms of the resulting condition numbers. We apply our results to the problem of approximately finding a feasible point in a polytope intersection in high-dimensions, and demonstrate the practical efficiency of our algorithms through empirical results.

Heterogeneity in federated learning (FL) is a critical and challenging aspect that significantly impacts model performance and convergence. In this paper, we propose a novel framework by formulating heterogeneous FL as a hierarchical optimization problem. This new framework captures both local and global training processes through a bilevel formulation and is capable of the following: (i) addressing client heterogeneity through a personalized learning framework; (ii) capturing the pre-training process on the server side; (iii) updating the global model through nonstandard aggregation; (iv) allowing for nonidentical local steps; and (v) capturing clients' local constraints. We design and analyze an implicit zeroth-order FL method (ZO-HFL), equipped with nonasymptotic convergence guarantees for both the server-agent and the individual client-agents, and asymptotic guarantees for both the server-agent and client-agents in an almost sure sense. Notably, our method does not rely on standard assumptions in heterogeneous FL, such as the bounded gradient dissimilarity condition. We implement our method on image classification tasks and compare with other methods under different heterogeneous settings.

RELATED WORKS Hand-Eye Calibration: Hand-eye calibration is a well-established problem in robotics that aims to estimate the relative pose between a camera and a robot's end-effector. It is typically addressed by capturing a series of images of a known calibration pattern (e.g., a checkerboard) using a camera rigidly mounted on the robot hand, and using both the images and the corresponding robot poses to compute the camera's extrinsic parameters. Different mathematical formulations exist for solving hand-eye calibration; a widely adopted approach involves solving the equation AX = XB, where X is the unknown rigid transformation describing the pose of the camera with respect to the robot, while A and B denote the relative motions of the end-effector (from robot kinematics) and the camera (from pattern observations), respectively [31], [36]-[38]. Several other approaches were proposed: Shah [39] formulated a closed-form solution for the hand-eye problem by using an algorithm based on Singular V alue Decomposition (SVD) and the Kronecker product to solve for rotation and translation separately, while Li et al. [40] used dual quaternions to solve them simultaneously overcoming the limitations of the Kronecker product. Wang et al. [23] extended hand-eye calibration to multi-camera setups by incorporating a common reference frame but required an external motion capture system, limiting its applicability to small setups. Andreff and Heller [41], [42] proposed two similar hand-eye calibration methods that leverage the Structure-from-Motion (SfM) paradigm to estimate camera motion and introduce a formulation for hand-eye calibration that includes a factor to metrically scale camera poses.

Using effective generalization capabilities of vision language models (VLMs) in context-specific dynamic tasks for embodied artificial intelligence remains a significant challenge. Although supervised fine-tuned models can better align with the real physical world, they still exhibit sluggish responses and hallucination issues in dynamically changing environments, necessitating further alignment. Existing post-SFT methods, reliant on reinforcement learning and chain-of-thought (CoT) approaches, are constrained by sparse rewards and action-only optimization, resulting in low sample efficiency, poor consistency, and model degradation. To address these issues, this paper proposes Thought-Centric Preference Optimization (TCPO) for effective embodied decision-making. Specifically, TCPO introduces a stepwise preference-based optimization approach, transforming sparse reward signals into richer step sample pairs. It emphasizes the alignment of the model's intermediate reasoning process, mitigating the problem of model degradation. Moreover, by incorporating Action Policy Consistency Constraint (APC), it further imposes consistency constraints on the model output. Experiments in the ALFWorld environment demonstrate an average success rate of 26.67%, achieving a 6% improvement over RL4VLM and validating the effectiveness of our approach in mitigating model degradation after fine-tuning. These results highlight the potential of integrating preference-based learning techniques with CoT processes to enhance the decision-making capabilities of vision-language models in embodied agents.

Decision-making under uncertainty is often considered in two stages: predicting the unknown parameters, and then optimizing decisions based on predictions. While traditional prediction-focused learning (PFL) treats these two stages separately, decision-focused learning (DFL) trains the predictive model by directly optimizing the decision quality in an end-to-end manner. However, despite using exact or well-approximated gradients, vanilla DFL often suffers from unstable convergence due to its flat-and-sharp loss landscapes. In contrast, PFL yields more stable optimization, but overlooks the downstream decision quality. To address this, we propose a simple yet effective approach: perturbing the decision loss gradient using the prediction loss gradient to construct an update direction. Our method requires no additional training and can be integrated with any DFL solvers. Using the sigmoid-like decaying parameter, we let the prediction loss gradient guide the decision loss gradient to train a predictive model that optimizes decision quality. Also, we provide a theoretical convergence guarantee to Pareto stationary point under mild assumptions. Empirically, we demonstrate our method across three stochastic optimization problems, showing promising results compared to other baselines. We validate that our approach achieves lower regret with more stable training, even in situations where either PFL or DFL struggles.

Mixture-of-Experts (MoE) has emerged as a promising architecture for modern large language models (LLMs). However, massive parameters impose heavy GPU memory (i.e., VRAM) demands, hindering the widespread adoption of MoE LLMs. Offloading the expert parameters to CPU RAM offers an effective way to alleviate the VRAM requirements for MoE inference. Existing approaches typically cache a small subset of experts in VRAM and dynamically prefetch experts from RAM during inference, leading to significant degradation in inference speed due to the poor cache hit rate and substantial expert loading latency. In this work, we propose MoEpic, an efficient MoE inference system with a novel expert split mechanism. Specifically, each expert is vertically divided into two segments: top and bottom. MoEpic caches the top segment of hot experts, so that more experts will be stored under the limited VRAM budget, thereby improving the cache hit rate. During each layer's inference, MoEpic predicts and prefetches the activated experts for the next layer. Since the top segments of cached experts are exempt from fetching, the loading time is reduced, which allows efficient transfer-computation overlap. Nevertheless, the performance of MoEpic critically depends on the cache configuration (i.e., each layer's VRAM budget and expert split ratio). To this end, we propose a divide-and-conquer algorithm based on fixed-point iteration for adaptive cache configuration. Extensive experiments on popular MoE LLMs demonstrate that MoEpic can save about half of the GPU cost, while lowering the inference latency by about 37.51%-65.73% compared to the baselines.