In the era of AI-driven science and engineering, we often want to design discrete objects in silico according to user-specified properties. For example, we may wish to design a protein to bind its target, arrange components within a circuit to minimize latency, or find materials with certain properties. Given a property predictive model, in silico design typically involves training a generative model over the design space (e.g., protein sequence space) to concentrate on designs with the desired properties. Distributional optimization -- which can be formalized as an estimation of distribution algorithm or as reinforcement learning policy optimization -- finds the generative model that maximizes an objective function in expectation. Optimizing a distribution over discrete-valued designs is in general challenging because of the combinatorial nature of the design space. However, many property predictors in scientific applications are decomposable in the sense that they can be factorized over design variables in a way that could in principle enable more effective optimization. For example, amino acids at a catalytic site of a protein may only loosely interact with amino acids of the rest of the protein to achieve maximal catalytic activity. Current distributional optimization algorithms are unable to make use of such decomposability structure. Herein, we propose and demonstrate use of a new distributional optimization algorithm, Decomposition-Aware Distributional Optimization (DADO), that can leverage any decomposability defined by a junction tree on the design variables, to make optimization more efficient. At its core, DADO employs a soft-factorized "search distribution" -- a learned generative model -- for efficient navigation of the search space, invoking graph message-passing to coordinate optimization across linked factors.

Humanoid robots represent a central frontier in embodied intelligence, as their anthropomorphic form enables natural deployment in humans' workspace. Brain-body co-design for humanoids presents a promising approach to realizing this potential by jointly optimizing control policies and physical morphology. Within this context, fall recovery emerges as a critical capability. It not only enhances safety and resilience but also integrates naturally with locomotion systems, thereby advancing the autonomy of humanoids. In this paper, we propose RoboCraft, a scalable humanoid co-design framework for fall recovery that iteratively improves performance through the coupled updates of control policy and morphology. A shared policy pretrained across multiple designs is progressively finetuned on high-performing morphologies, enabling efficient adaptation without retraining from scratch. Concurrently, morphology search is guided by human-inspired priors and optimization algorithms, supported by a priority buffer that balances reevaluation of promising candidates with the exploration of novel designs. Experiments show that RoboCraft achieves an average performance gain of 44.55% on seven public humanoid robots, with morphology optimization drives at least 40% of improvements in co-designing four humanoid robots, underscoring the critical role of humanoid co-design.

The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled quantitative abstraction. This work develops a unified theory of such abstraction by integrating category theory, coalgebra, quantitative logic, and optimal transport, centred on a canonical $\varepsilon$-quotient of the behavioral pseudo-metric with a universal property: among all abstractions that collapse behavioral differences below $\varepsilon$, it is the most detailed, and every other abstraction achieving the same discounted value-loss guarantee factors uniquely through it. Categorically, a quotient functor $Q_\varepsilon$ from a category of probabilistic systems to a category of metric specifications admits, via the Special Adjoint Functor Theorem, a right adjoint $R_\varepsilon$, yielding an adjunction $Q_\varepsilon \dashv R_\varepsilon$ that formalizes a duality between abstraction and realization; logically, a quantitative modal $μ$-calculus with separate reward and transition modalities is shown, for a broad class of systems, to be expressively complete for the behavioral pseudo-metric, with a countable fully abstract fragment suitable for computation. The theory is developed coalgebraically over Polish spaces and the Giry monad and validated on finite-state models using optimal-transport solvers, with experiments corroborating the predicted contraction properties and structural stability and aligning with the theoretical value-loss bounds, thereby providing a rigorous foundation for quantitative state abstraction and representation learning in probabilistic domains.

Data sharing ecosystems connect providers, consumers, and intermediaries to facilitate the exchange and use of data for a wide range of downstream tasks. In sensitive domains such as healthcare, privacy is enforced as a hard constraint, any shared data must satisfy a minimum privacy threshold. However, among all masking configurations that meet this requirement, the utility of the masked data can vary significantly, posing a key challenge: how to efficiently select the optimal configuration that preserves maximum utility. This paper presents Aegis, a middleware framework that selects optimal masking configurations for machine learning datasets with features and class labels. Aegis incorporates a utility optimizer that minimizes predictive utility deviation, quantifying shifts in feature label correlations due to masking. Our framework leverages limited data summaries (such as 1D histograms) or none to estimate the feature label joint distribution, making it suitable for scenarios where raw data is inaccessible due to privacy restrictions. To achieve this, we propose a joint distribution estimator based on iterative proportional fitting, which allows supporting various feature label correlation quantification methods such as mutual information, chi square, or g3. Our experimental evaluation of real world datasets shows that Aegis identifies optimal masking configurations over an order of magnitude faster, while the resulting masked datasets achieve predictive performance on downstream ML tasks on par with baseline approaches and complements privacy anonymization data masking techniques.

For precise, efficient, and safe drone landings, ground platforms should real-time, accurately locate descending drones and guide them to designated spots. While mmWave sensing combined with cameras improves localization accuracy, lower sampling frequency of traditional frame cameras compared to mmWave radar creates bottlenecks in system throughput. In this work, we upgrade traditional frame camera with event camera, a novel sensor that harmonizes in sampling frequency with mmWave radar within ground platform setup, and introduce mmE-Loc, a high-precision, low-latency ground localization system designed for precise drone landings. To fully exploit the \textit{temporal consistency} and \textit{spatial complementarity} between these two modalities, we propose two innovative modules: \textit{(i)} the Consistency-instructed Collaborative Tracking module, which further leverages the drone's physical knowledge of periodic micro-motions and structure for accurate measurements extraction, and \textit{(ii)} the Graph-informed Adaptive Joint Optimization module, which integrates drone motion information for efficient sensor fusion and drone localization. Real-world experiments conducted in landing scenarios with a drone delivery company demonstrate that mmE-Loc significantly outperforms state-of-the-art methods in both accuracy and latency.

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our analysis demonstrates that, by fixing the support set, the global solution of the minimization subproblem for the proximal linearization of the objective function can be computed in closed form with at most $n$ nonzero entries. Exploiting this structural property offers a powerful avenue for dramatically enhancing computational efficiency. Guided by this insight, we propose a support-set algorithm preserving strictly the feasibility of iterates. A central ingredient is a strategically devised update scheme for support sets that adjusts the placement of nonzero entries. We establish the global convergence of the support-set algorithm to a first-order stationary point, and show that its iteration complexity required to reach an $ε$-approximate first-order stationary point is $O (ε^{-2})$. Numerical results are strongly in favor of our algorithm in real-world applications, including nonnegative PCA, clustering, and community detection.

Hyperparameter optimization (HPO), for example, based on Bayesian optimization (BO), supports users in designing models well-suited for a given dataset. HPO has proven its effectiveness on several applications, ranging from classical machine learning for tabular data to deep neural networks for computer vision and transformers for natural language processing. However, HPO still sometimes lacks acceptance by machine learning experts due to its black-box nature and limited user control. Addressing this, first approaches have been proposed to initialize BO methods with expert knowledge. However, these approaches do not allow for online steering during the optimization process. In this paper, we introduce a novel method that enables repeated interventions to steer BO via user input, specifying expert knowledge and user preferences at runtime of the HPO process in the form of prior distributions. To this end, we generalize an existing method, $π$BO, preserving theoretical guarantees. We also introduce a misleading prior detection scheme, which allows protection against harmful user inputs. In our experimental evaluation, we demonstrate that our method can effectively incorporate multiple priors, leveraging informative priors, whereas misleading priors are reliably rejected or overcome. Thereby, we achieve competitiveness to unperturbed BO.

Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of kernel discrepancies, selecting an m-element subset from a large population of size $n \gg m$. We introduce a novel subset selection algorithm applicable to general kernel discrepancies to efficiently generate low-discrepancy samples from both the uniform distribution on the unit hypercube, the traditional setting of classical QMC, and from more general distributions $F$ with known density functions by employing the kernel Stein discrepancy. We also explore the relationship between the classical $L_2$ star discrepancy and its $L_\infty$ counterpart.

Proximal Policy Optimization (PPO) is widely regarded as one of the most successful deep reinforcement learning algorithms, known for its robustness and effectiveness across a range of problems. The PPO objective encourages the importance ratio between the current and behavior policies to move to the "right" direction -- starting from importance sampling ratios equal to 1, increasing the ratios for actions with positive advantages and decreasing those with negative advantages. A clipping function is introduced to prevent over-optimization when updating the importance ratio in these "right" direction regions. Many PPO variants have been proposed to extend its success, most of which modify the objective's behavior by altering the clipping in the "right" direction regions. However, due to randomness in the rollouts and stochasticity of the policy optimization, we observe that the ratios frequently move to the "wrong" direction during the PPO optimization. This is a key factor hindering the improvement of PPO, but it has been largely overlooked. To address this, we propose the Directional-Clamp PPO algorithm (DClamp-PPO), which further penalizes the actions going to the strict "wrong" direction regions, where the advantage is positive (negative) and importance ratio falls below (above) $1 - β$ ($1+β$), for a tunable parameter $β\in (0, 1)$. The penalty is by enforcing a steeper loss slope, i.e., a clamp, in those regions. We demonstrate that DClamp-PPO consistently outperforms PPO, as well as its variants, by focusing on modifying the objective's behavior in the "right" direction, across various MuJoCo environments, using different random seeds. The proposed method is shown, both theoretically and empirically, to better avoid "wrong" direction updates while keeping the importance ratio closer to 1.

Diverse learning algorithms, optimization methods, and natural selection share a common mathematical structure, despite their apparent differences. Here I show that a simple notational partitioning of change by the Price equation reveals a universal force-metric-bias (FMB) law: $Δ\mathbfθ = \mathbf{M}\,\mathbf{f} + \mathbf{b} + \mathbfξ$. The force $\mathbf{f}$ drives improvement in parameters, $Δ\mathbfθ$, in proportion to the slope of performance with respect to the parameters. The metric $\mathbf{M}$ rescales movement by inverse curvature. The bias $\mathbf{b}$ adds momentum or changes in the frame of reference. The noise $\mathbfξ$ enables exploration. This framework unifies natural selection, Bayesian updating, Newton's method, stochastic gradient descent, stochastic Langevin dynamics, Adam optimization, and most other algorithms as special cases of the same underlying process. The Price equation also reveals why Fisher information, Kullback-Leibler divergence, and d'Alembert's principle arise naturally in learning dynamics. By exposing this common structure, the FMB law provides a principled foundation for understanding, comparing, and designing learning algorithms across disciplines.