In this paper, we derive variational inference upper-bounds on the log-partition function of pairwise Markov random fields on the Boolean hypercube, based on quantum relaxations of the Kullback-Leibler divergence. We then propose an efficient algorithm to compute these bounds based on primal-dual optimization. An improvement of these bounds through the use of ''hierarchies,'' similar to sum-of-squares (SoS) hierarchies is proposed, and we present a greedy algorithm to select among these relaxations. We carry extensive numerical experiments and compare with state-of-the-art methods for this inference problem.

Exploration is a crucial and distinctive aspect of reinforcement learning (RL) that remains a fundamental open problem. Several methods have been proposed to tackle this challenge. Commonly used methods inject random noise directly into the actions, indirectly via entropy maximization, or add intrinsic rewards that encourage the agent to steer to novel regions of the state space. Another previously seen idea is to use the Bellman error as a separate optimization objective for exploration. In this paper, we introduce three modifications to stabilize the latter and arrive at a deterministic exploration policy. Our separate exploration agent is informed about the state of the exploitation, thus enabling it to account for previous experiences. Further components are introduced to make the exploration objective agnostic toward the episode length and to mitigate instability introduced by far-off-policy learning. Our experimental results show that our approach can outperform $\varepsilon$-greedy in dense and sparse reward settings.

Recent advances in quadrupedal locomotion have focused on improving stability and performance across diverse environments. However, existing methods often lack adequate safety analysis and struggle to adapt to varying payloads and complex terrains, typically requiring extensive tuning. To overcome these challenges, we propose a Chance-Constrained Model Predictive Control (CCMPC) framework that explicitly models payload and terrain variability as distributions of parametric and additive disturbances within the single rigid body dynamics (SRBD) model. Our approach ensures safe and consistent performance under uncertain dynamics by expressing the model friction cone constraints, which define the feasible set of ground reaction forces, as chance constraints. Moreover, we solve the resulting stochastic control problem using a computationally efficient quadratic programming formulation. Extensive Monte Carlo simulations of quadrupedal locomotion across varying payloads and complex terrains demonstrate that CCMPC significantly outperforms two competitive benchmarks: Linear MPC (LMPC) and MPC with hand-tuned safety margins to maintain stability, reduce foot slippage, and track the center of mass. Hardware experiments on the Unitree Go1 robot show successful locomotion across various indoor and outdoor terrains with unknown loads exceeding 50% of the robot body weight, despite no additional parameter tuning. A video of the results and accompanying code can be found at: https://cc-mpc.github.io/.

The data-driven drug design problem can be formulated as an optimization task of a potentially expensive black-box objective function over a huge high-dimensional and structured molecular space. The junction tree variational autoencoder (JTVAE) has been shown to be an efficient generative model that can be used for suggesting legitimate novel drug-like small molecules with improved properties. While the performance of the generative molecular design (GMD) scheme strongly depends on the initial training data, one can improve its sampling efficiency for suggesting better molecules with enhanced properties by optimizing the latent space. In this work, we propose how mechanistic models - such as pathway models described by differential equations - can be used for effective latent space optimization(LSO) of JTVAEs and other similar models for GMD. To demonstrate the potential of our proposed approach, we show how a pharmacodynamic model, assessing the therapeutic efficacy of a drug-like small molecule by predicting how it modulates a cancer pathway, can be incorporated for effective LSO of data-driven models for GMD.

This paper delves into the continuous post-training optimization methods for small language models, and proposes a continuous post-training alignment data construction method for small language models. The core of this method is based on the data guidance of large models, optimizing the diversity and accuracy of alignment data. In addition, to verify the effectiveness of the methods in this paper, we used Qwen2-0.5B-Instruct model as the baseline model for small language models, using the alignment dataset constructed by our proposed method, we trained and compared several groups of experiments, including SFT (Supervised Fine Tuning) post-training experiment and KTO (Kahneman Tversky optimization) post-training experiment, as well as SFT-KTO two-stage post-training experiment and model weight fusion experiment. Finally, we evaluated and analyzed the performance of post-training models, and confirmed that the continuous post-training optimization method proposed by us can significantly improve the performance of small language models.

Although nearly 20 years have passed since its conception, the feasibility pump algorithm remains a widely used heuristic to find feasible primal solutions to mixed-integer linear problems. Many extensions of the initial algorithm have been proposed. Yet, its core algorithm remains centered around two key steps: solving the linear relaxation of the original problem to obtain a solution that respects the constraints, and rounding it to obtain an integer solution. This paper shows that the traditional feasibility pump and many of its follow-ups can be seen as gradient-descent algorithms with specific parameters. A central aspect of this reinterpretation is observing that the traditional algorithm differentiates the solution of the linear relaxation with respect to its cost. This reinterpretation opens many opportunities for improving the performance of the original algorithm. We study how to modify the gradient-update step as well as extending its loss function. We perform extensive experiments on MIPLIB instances and show that these modifications can substantially reduce the number of iterations needed to find a solution.

Multi-objective Bayesian optimization (MBO) plays a critical role in various scientific fields, particularly where experimental efficiency and precision are paramount. In drug discovery, for example, researchers must navigate a vast experimental space, balancing multiple objectives like maximizing therapeutic efficacy while minimizing toxicity and adverse effects (Fromer and Coley, 2023). The challenge lies not only in identifying promising drug candidates but also in meeting stringent regulatory and safety requirements, which impose additional constraints on the optimization process (Mellinghoff and Cloughesy, 2022). A failure to meet these regulatory and safety constraints can lead to significant delays in clinical trials or even abandonment of potential drug candidates. Similarly, in hyper-parameter optimization for machine learning models, there is a need to balance model accuracy, recall, and robustness to distribution shift (Gardner et al., 2019). Here, efficient exploration of hyper-parameter space must also respect practical constraints, such as avoiding configurations that lead to excessively high training times or resource overuse (Karl et al., 2023). Those practical considerations motivate the constrained multi-objective Bayesian optimization (Fernández-Sánchez et al., 2023; Hernández-Lobato et al., 2016) beyond MBO. Research in Bayesian Optimization (BO) has mainly focused on unconstrained problems, with Constrained Bayesian Optimization (CBO) evolving from early work by Schonlau et al. (1998). Subsequent efforts introduced posterior sampling (Eriksson and Poloczek, 2021) and informationbased methods (Hernández-Lobato et al., 2014; Wang and Jegelka, 2017) to improve scalability and feasibility analysis (Hernández-Lobato et al., 2015; Perrone et al., 2019; Takeno et al., 2022).

We study the analysis of all the movements of the population on the basis of their mobility from one node to another, to observe, measure, and predict the impact of traffic according to this mobility. The frequency of congestion on roads directly or indirectly impacts our economic or social welfare. Our work focuses on exploring some machine learning methods to predict (with a certain probability) traffic in a multimodal transportation network from population mobility data. We analyze the observation of the influence of people's movements on the transportation network and make a likely prediction of congestion on the network based on this observation (historical basis).

We study the problem of matching markets with ties, where one side of the market does not necessarily have strict preferences over members at its other side. For example, workers do not always have strict preferences over jobs, students can give the same ranking for different schools and more. In particular, assume w.l.o.g. that workers' preferences are determined by their utility from being matched to each job, which might admit ties. Notably, in contrast to classical two-sided markets with strict preferences, there is no longer a single stable matching that simultaneously maximizes the utility for all workers. We aim to guarantee each worker the largest possible share from the utility in her best possible stable matching. We call the ratio between the worker's best possible stable utility and its assigned utility the \emph{Optimal Stable Share} (OSS)-ratio. We first prove that distributions over stable matchings cannot guarantee an OSS-ratio that is sublinear in the number of workers. Instead, randomizing over possibly non-stable matchings, we show how to achieve a tight logarithmic OSS-ratio. Then, we analyze the case where the real utility is not necessarily known and can only be approximated. In particular, we provide an algorithm that guarantees a similar fraction of the utility compared to the best possible utility. Finally, we move to a bandit setting, where we select a matching at each round and only observe the utilities for matches we perform. We show how to utilize our results for approximate utilities to gracefully interpolate between problems without ties and problems with statistical ties (small suboptimality gaps).

To alleviate computational load on RSUs and cloud platforms, reduce communication bandwidth requirements, and provide a more stable vehicular network service, this paper proposes an optimized pinning control approach for heterogeneous multi-network vehicular ad-hoc networks (VANETs). In such networks, vehicles participate in multiple task-specific networks with asymmetric coupling and dynamic topologies. We first establish a rigorous theoretical foundation by proving the stability of pinning control strategies under both single and multi-network conditions, deriving sufficient stability conditions using Lyapunov theory and linear matrix inequalities (LMIs). Building on this theoretical groundwork, we propose an adaptive genetic algorithm tailored to select optimal pinning nodes, effectively balancing LMI constraints while prioritizing overlapping nodes to enhance control efficiency. Extensive simulations across various network scales demonstrate that our approach achieves rapid consensus with a reduced number of control nodes, particularly when leveraging network overlaps. This work provides a comprehensive solution for efficient control node selection in complex vehicular networks, offering practical implications for deploying large-scale intelligent transportation systems.