The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated approximation methods like entropy-regularized optimal transport, downsampling, and subsampling, which trade accuracy for computational efficiency. In this paper, we consider the challenge of computing efficient approximations to the Wasserstein metric that also serve as strict upper or lower bounds. Focusing on discrete measures on regular grids, our approach involves formulating and exactly solving a Kantorovich problem on a coarse grid using a quantized measure and specially designed cost matrix, followed by an upscaling and correction stage. This is done either in the primal or dual space to obtain valid upper and lower bounds on the Wasserstein metric of the full-resolution inputs. We evaluate our methods on the DOTmark optimal transport images benchmark, demonstrating a 10x-100x speedup compared to entropy-regularized OT while keeping the approximation error below 2%.

Causal Discovery plays a pivotal role in revealing relationships among observed variables, particularly in the temporal setup. While the majority of CD methods rely on synthetic data for evaluation, and recently for training, these fall short in accurately mirroring real-world scenarios; an effect even more evident in temporal data. Generation techniques depending on simplified assumptions on causal structure, effects and time, limit the quality and diversity of the simulated data. In this work, we introduce Temporal Causal-based Simulation (TCS), a robust framework for generating realistic time-series data and their associated temporal causal graphs. The approach is structured in three phases: estimating the true lagged causal structure of the data, approximating the functional dependencies between variables and learning the noise distribution of the corresponding causal model, each part of which can be explicitly tailored based on data assumptions and characteristics. Through an extensive evaluation process, we highlight that single detection methods for generated data discrimination prove inadequate, accentuating it as a multifaceted challenge. For this, we detail a Min-max optimization phase that draws on AutoML techniques. Our contributions include a flexible, model-agnostic pipeline for generating realistic temporal causal data, a thorough evaluation setup which enhances the validity of the generated datasets and insights into the challenges posed by realistic data generation. Through experiments involving not only real but also semi-synthetic and purely synthetic datasets, we demonstrate that while sampling realistic causal data remains a complex task, our method enriches the domain of generating sensible causal-based temporal data.

Standard A/B tests in online experiments face statistical power challenges when testing multiple candidates simultaneously, while adaptive experimental designs (AED) alone fall short in inferring experiment statistics such as the average treatment effect, especially with many metrics (e.g., revenue, safety) and heterogeneous variances. This paper proposes a fixed-budget multi-metric AED framework with a two-phase structure: an adaptive exploration phase to identify the best treatment, and a validation phase with an A/B test to verify the treatment's quality and infer statistics. We propose SHRVar, which generalizes sequential halving (SH) (Karnin et al., 2013) with a novel relative-variance-based sampling and an elimination strategy built on reward z-values. It achieves a provable error probability that decreases exponentially, where the exponent generalizes the complexity measure for SH (Karnin et al., 2013) and SHVar (Lalitha et al., 2023) with homogeneous and heterogeneous variances, respectively. Numerical experiments verify our analysis and demonstrate the superior performance of this new framework.

Link functions, which characterize how human preferences are generated from the value function of an RL problem, are a crucial component in designing RLHF algorithms. Almost all RLHF algorithms, including state-of-the-art ones in empirical studies such as DPO and PPO, assume the link function is known to the agent (e.g., a logistic function according to the Bradley-Terry model), which is arguably unrealistic considering the complex nature of human preferences. To avoid link function mis-specification, this paper studies general RLHF problems with unknown link functions. We propose a novel policy optimization algorithm called ZSPO based on a new zeroth-order policy optimization method, where the key is to use human preference to construct a parameter update direction that is positively correlated with the true policy gradient direction. ZSPO achieves it by estimating the sign of the value function difference instead of estimating the gradient from the value function difference, so it does not require knowing the link function. Under mild conditions, ZSPO converges to a stationary policy with a polynomial convergence rate depending on the number of policy iterations and trajectories per iteration. Numerical results also show the superiority of ZSPO under link function mismatch.

Federated learning faces severe communication bottlenecks due to the high dimensionality of model updates. Communication compression with contractive compressors (e.g., Top-K) is often preferable in practice but can degrade performance without proper handling. Error feedback (EF) mitigates such issues but has been largely restricted for smooth, unconstrained problems, limiting its real-world applicability where non-smooth objectives and safety constraints are critical. We advance our understanding of EF in the canonical non-smooth convex setting by establishing new lower complexity bounds for first-order algorithms with contractive compression. Next, we propose Safe-EF, a novel algorithm that matches our lower bound (up to a constant) while enforcing safety constraints essential for practical applications. Extending our approach to the stochastic setting, we bridge the gap between theory and practical implementation. Extensive experiments in a reinforcement learning setup, simulating distributed humanoid robot training, validate the effectiveness of Safe-EF in ensuring safety and reducing communication complexity.

As UAV popularity soars, so does the mission planning associated with it. The classical approaches suffer from the triple problems of decoupled of task assignment and path planning, poor real-time performance and limited adaptability. Aiming at these challenges, this paper proposes a dynamic real-time multi-UAV collaborative mission planning algorithm based on Dubins paths under a distributed formation structure. Dubins path with multiple advantages bridges the gap between task assignment and path planning, leading to a coupled solution for mission planning. Then, a series of acceleration techniques, task clustering preprocessing, highly efficient distance cost functions, low-complexity and less iterative task allocation strategies, are employed to guarantee the real-time performance of the algorithms. To cope with different emergencies and their simultaneous extremes, real-time planning of emerging tasks and mission replanning due to the reduction of available UAVs are appropriately handled. Finally, the developed algorithm is comprehensively exemplified and studied through simulations, highlighting that the proposed method only sacrifices 9.57% of the path length, while achieving a speed improvement of 4-5 orders of magnitude over the simulated annealing method, with a single mission planning of about 0.0003s.

We propose a training-free, Vision-Language Model (VLM)-guided approach for efficiently generating trajectories to facilitate target inspection planning based on text descriptions. Unlike existing Vision-and-Language Navigation (VLN) methods designed for general agents in unknown environments, our approach specifically targets the efficient inspection of known scenes, with widespread applications in fields such as medical, marine, and civil engineering. Leveraging VLMs, our method first extracts points of interest (POIs) from the text description, then identifies a set of waypoints from which POIs are both salient and align with the spatial constraints defined in the prompt. Next, we interact with the VLM to iteratively refine the trajectory, preserving the visibility and prominence of the POIs. Further, we solve a Traveling Salesman Problem (TSP) to find the most efficient visitation order that satisfies the order constraint implied in the text description. Finally, we apply trajectory optimization to generate smooth, executable inspection paths for aerial and underwater vehicles. We have evaluated our method across a series of both handcrafted and real-world scanned environments. The results demonstrate that our approach effectively generates inspection planning trajectories that adhere to user instructions.

Recent studies, including DeepSeek-R1 and Kimi-k1.5, have demonstrated that reinforcement learning with rule-based, binary-valued reward functions can significantly enhance the reasoning capabilities of large language models. These models primarily utilize REINFORCE-based policy optimization techniques, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation remains: current policy optimization methods either neglect reward normalization or employ static normalization strategies, which fail to adapt to the dynamic nature of policy updates during training. This may result in unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel policy optimization method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. BNPO aligns the normalization with the changing policy distribution, enabling more precise and lower-variance gradient estimation, which in turn promotes stable training dynamics. We provide theoretical analysis demonstrating BNPO's variance-reducing properties and show that it generalizes both REINFORCE and GRPO under binary-valued reward settings. Furthermore, we introduce an advantage decomposition mechanism to extend BNPO's applicability to more complex reward systems. Experimental results confirm that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks. The code is available at https://github.com/changyi7231/BNPO.

Hybrid parallelism techniques are essential for efficiently training large language models (LLMs). Nevertheless, current automatic parallel planning frameworks often overlook the simultaneous consideration of node heterogeneity and dynamic network topology changes, limiting their effectiveness in practical applications. In this paper, we address these limitations by modeling heterogeneous nodes within dynamically changing network environments and leveraging simulation-based strategies to determine optimal parallel configurations. Our approach enables fine-grained workload allocation tailored for heterogeneous nodes and complex network scenarios, achieving performance competitive with state-of-the-art methods under regular and stable network conditions. Additionally, we introduce a strategy pruning technique to rapidly discard infeasible parallel configurations, substantially reducing the search space and accelerating the search process through parallel execution within the simulator. Preliminary evaluations confirm that our method notably enhances training performance on heterogeneous nodes and demonstrates improved adaptability in complex, dynamic scenarios such as cloud computing environments.

This paper addresses the slow policy optimization convergence of Monte Carlo Probabilistic Inference for Learning Control (MC-PILCO), a state-of-the-art model-based reinforcement learning (MBRL) algorithm, by integrating it with iterative Linear Quadratic Regulator (iLQR), a fast trajectory optimization method suitable for nonlinear systems. The proposed method, Exploration-Boosted MC-PILCO (EB-MC-PILCO), leverages iLQR to generate informative, exploratory trajectories and initialize the policy, significantly reducing the number of required optimization steps. Experiments on the cart-pole task demonstrate that EB-MC-PILCO accelerates convergence compared to standard MC-PILCO, achieving up to $\bm{45.9\%}$ reduction in execution time when both methods solve the task in four trials. EB-MC-PILCO also maintains a $\bm{100\%}$ success rate across trials while solving the task faster, even in cases where MC-PILCO converges in fewer iterations.