In robotic planetary surface exploration, strategic mobility planning is an important task that involves finding candidate long-distance routes on orbital maps and identifying segments with uncertain traversability. Then, expert human operators establish safe, adaptive traverse plans based on the actual navigation difficulties encountered in these uncertain areas. In this paper, we formalize this challenge as a new, risk-averse variant of the Canadian Traveller Problem (CTP) tailored to global planetary mobility. The objective is to find a traverse policy minimizing a conditional value-at-risk (CVaR) criterion, which is a risk measure with an intuitive interpretation. We propose a novel search algorithm that finds exact CVaR-optimal policies. Our approach leverages well-established optimal AND-OR search techniques intended for (risk-agnostic) expectation minimization and extends these methods to the risk-averse domain. We validate our approach through simulated long-distance planetary surface traverses; we employ real orbital maps of the Martian surface to construct problem instances and use terrain maps to express traversal probabilities in uncertain regions. Our results illustrate different adaptive decision-making schemes depending on the level of risk aversion. Additionally, our problem setup allows accounting for traversability correlations between similar areas of the environment. In such a case, we empirically demonstrate how information-seeking detours can mitigate risk.

This paper formalizes an emerging learning paradigm that uses a trained model as a reference to guide and enhance the training of a target model through strategic data selection or weighting, named $\textbf{model steering}$. While ad-hoc methods have been used in various contexts, including the training of large foundation models, its underlying principles remain insufficiently understood, leading to sub-optimal performance. In this work, we propose a theory-driven framework for model steering called $\textbf{DRRho risk minimization}$, which is rooted in Distributionally Robust Optimization (DRO). Through a generalization analysis, we provide theoretical insights into why this approach improves generalization and data efficiency compared to training without a reference model. To the best of our knowledge, this is the first time such theoretical insights are provided for the new learning paradigm, which significantly enhance our understanding and practice of model steering. Building on these insights and the connection between contrastive learning and DRO, we introduce a novel method for Contrastive Language-Image Pretraining (CLIP) with a reference model, termed DRRho-CLIP. Extensive experiments validate the theoretical insights, reveal a superior scaling law compared to CLIP without a reference model, and demonstrate its strength over existing heuristic approaches.

Decision-focused learning (DFL) is an increasingly popular paradigm for training predictive models whose outputs are used in decision-making tasks. Instead of merely optimizing for predictive accuracy, DFL trains models to directly minimize the loss associated with downstream decisions. This end-to-end strategy holds promise for tackling complex combinatorial problems; however, existing studies focus solely on scenarios where a fixed batch of data is available and the objective function does not change over time. We instead investigate DFL in dynamic environments where the objective function and data distribution evolve over time. This setting is challenging because the objective function has zero or undefined gradients -- which prevents the use of standard first-order optimization methods -- and is generally non-convex. To address these difficulties, we (i) regularize the objective to make it differentiable and (ii) make use of the optimism principle, based on a near-optimal oracle along with an appropriate perturbation. This leads to a practical online algorithm for which we establish bounds on the expected dynamic regret, both when the decision space is a simplex and when it is a general bounded convex polytope. Finally, we demonstrate the effectiveness of our algorithm by comparing its performance with a classic prediction-focused approach on a simple knapsack experiment.

This paper introduces a new constraint-free concave dual formulation for the Wasserstein barycenter. Tailoring the vanilla dual gradient ascent algorithm to the Sobolev geometry, we derive a scalable Sobolev gradient ascent (SGA) algorithm to compute the barycenter for input distributions supported on a regular grid. Despite the algorithmic simplicity, we provide a global convergence analysis that achieves the same rate as the classical subgradient descent methods for minimizing nonsmooth convex functions in the Euclidean space. A central feature of our SGA algorithm is that the computationally expensive $c$-concavity projection operator enforced on the Kantorovich dual potentials is unnecessary to guarantee convergence, leading to significant algorithmic and theoretical simplifications over all existing primal and dual methods for computing the exact barycenter. Our numerical experiments demonstrate the superior empirical performance of SGA over the existing optimal transport barycenter solvers.

Maximum mean discrepancy (MMD) has been widely employed to measure the distance between probability distributions. In this paper, we propose using MMD to solve continuous multi-objective optimization problems (MOPs). For solving MOPs, a common approach is to minimize the distance (e.g., Hausdorff) between a finite approximate set of the Pareto front and a reference set. Viewing these two sets as empirical measures, we propose using MMD to measure the distance between them. To minimize the MMD value, we provide the analytical expression of its gradient and Hessian matrix w.r.t. the search variables, and use them to devise a novel set-oriented, MMD-based Newton (MMDN) method. Also, we analyze the theoretical properties of MMD's gradient and Hessian, including the first-order stationary condition and the eigenspectrum of the Hessian, which are important for verifying the correctness of MMDN. To solve complicated problems, we propose hybridizing MMDN with multiobjective evolutionary algorithms (MOEAs), where we first execute an EA for several iterations to get close to the global Pareto front and then warm-start MMDN with the result of the MOEA to efficiently refine the approximation. We empirically test the hybrid algorithm on 11 widely used benchmark problems, and the results show the hybrid (MMDN + MOEA) can achieve a much better optimization accuracy than EA alone with the same computation budget.

Sim-to-real discrepancies hinder learning-based policies from achieving high-precision tasks in the real world. While Domain Randomization (DR) is commonly used to bridge this gap, it often relies on heuristics and can lead to overly conservative policies with degrading performance when not properly tuned. System Identification (Sys-ID) offers a targeted approach, but standard techniques rely on differentiable dynamics and/or direct torque measurement, assumptions that rarely hold for contact-rich legged systems. To this end, we present SPI-Active (Sampling-based Parameter Identification with Active Exploration), a two-stage framework that estimates physical parameters of legged robots to minimize the sim-to-real gap. SPI-Active robustly identifies key physical parameters through massive parallel sampling, minimizing state prediction errors between simulated and real-world trajectories. To further improve the informativeness of collected data, we introduce an active exploration strategy that maximizes the Fisher Information of the collected real-world trajectories via optimizing the input commands of an exploration policy. This targeted exploration leads to accurate identification and better generalization across diverse tasks. Experiments demonstrate that SPI-Active enables precise sim-to-real transfer of learned policies to the real world, outperforming baselines by 42-63% in various locomotion tasks.

Adversarial Patrolling games form a subclass of Security games where a Defender moves between locations, guarding vulnerable targets. The main algorithmic problem is constructing a strategy for the Defender that minimizes the worst damage an Attacker can cause. We focus on the class of finite-memory (also known as regular) Defender's strategies that experimentally outperformed other competing classes. A finite-memory strategy can be seen as a positional strategy on a finite set of states. Each state consists of a pair of a location and a certain integer value--called memory. Existing algorithms improve the transitional probabilities between the states but require that the available memory size itself is assigned at each location manually. Choosing the right memory assignment is a well-known open and hard problem that hinders the usability of finite-memory strategies. We solve this issue by developing a general method that iteratively changes the memory assignment. Our algorithm can be used in connection with \emph{any} black-box strategy optimization tool. We evaluate our method on various experiments and show its robustness by solving instances of various patrolling models.

In this paper we propose for the first time the hyperparameter optimization (HPO) algorithm POCAII. POCAII differs from the Hyperband and Successive Halving literature by explicitly separating the search and evaluation phases and utilizing principled approaches to exploration and exploitation principles during both phases. Such distinction results in a highly flexible scheme for managing a hyperparameter optimization budget by focusing on search (i.e., generating competing configurations) towards the start of the HPO process while increasing the evaluation effort as the HPO comes to an end. POCAII was compared to state of the art approaches SMAC, BOHB and DEHB. Our algorithm shows superior performance in low-budget hyperparameter optimization regimes. Since many practitioners do not have exhaustive resources to assign to HPO, it has wide applications to real-world problems. Moreover, the empirical evidence showed how POCAII demonstrates higher robustness and lower variance in the results. This is again very important when considering realistic scenarios with extremely expensive models to train.

We introduce proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a principled foundation for optimal transport proximals and proximal optimization methods frequently used in generative modeling. We explore its mathematical properties, including smoothness, boundedness, and computational tractability, and establish connections to primal-dual formulation and adversarial learning. Building on the Benamou-Brenier dynamic formulation of optimal transport cost, we also establish a dynamic formulation for proximal OT divergences. The resulting dynamic formulation is a first order mean-field game whose optimality conditions are governed by a pair of nonlinear partial differential equations, a backward Hamilton-Jacobi and a forward continuity partial differential equations.

In cloud services, virtual machine (VM) scheduling is a typical Online Dynamic Multidimensional Bin Packing (ODMBP) problem, characterized by large-scale complexity and fluctuating demands. Traditional optimization methods struggle to adapt to real-time changes, domain-expert-designed heuristic approaches suffer from rigid strategies, and existing learning-based methods often lack generalizability and interpretability. To address these limitations, this paper proposes a hierarchical language agent framework named MiCo, which provides a large language model (LLM)-driven heuristic design paradigm for solving ODMBP. Specifically, ODMBP is formulated as a Semi-Markov Decision Process with Options (SMDP-Option), enabling dynamic scheduling through a two-stage architecture, i.e., Option Miner and Option Composer. Option Miner utilizes LLMs to discover diverse and useful non-context-aware strategies by interacting with constructed environments. Option Composer employs LLMs to discover a composing strategy that integrates the non-context-aware strategies with the contextual ones. Extensive experiments on real-world enterprise datasets demonstrate that MiCo achieves a 96.9\% competitive ratio in large-scale scenarios involving more than 10,000 virtual machines. It maintains high performance even under nonstationary request flows and diverse configurations, thus validating its effectiveness in complex and large-scale cloud environments.