In complex real-world settings, optimization is challenged by the presence of diverse models of differing fidelity. In many optimization problems, a single model is treated as the most accurate representation of the underlying system, while other models are evaluated primarily by their agreement with this presumed most accurate model. Yet in real-world applications, model accuracy is rarely known a priori and assuming a single most accurate model can be misleading. This paper addresses this gap by proposing a flexible set-based optimization methodology called Set-Based Optimization with Multiple Models (S-BOMM) that works with multiple models without the assumption of a most accurate high-fidelity model. Unlike traditional optimization approaches that focus on finding an optimal solution according to the high-fidelity model, our methodology utilizes consistency between models to identify good solutions across multiple models. A probabilistic analysis of the consistency method is provided that bounds the likelihood of the methodology producing correct or incorrect results. Empirical results demonstrate the effectiveness of S-BOMM on test problems. By focusing on the consistency across models rather than relying on a single best solution, this set-based approach offers a practical alternative to optimization problems where multiple models must be considered without assuming a single most accurate high-fidelity model.

Existing risk-aware multi-armed bandit models typically focus on risk measures of individual options such as variance. As a result, they cannot be directly applied to important real-world online decision making problems with correlated options. In this paper, we propose a novel Continuous Mean-Covariance Bandit (CMCB) model to explicitly take into account option correlation. Specifically, in CMCB, there is a learner who sequentially chooses weight vectors on given options and observes random feedback according to the decisions. The agent's objective is to achieve the best trade-off between reward and risk, measured with option covariance.

We propose a novel algorithmic framework that is tractable, asymptotically consistent,andsuperiortocomparable methodsonexampleproblems.

Retrosynthesis prediction aims to infer the reactant molecule based on a given product molecule, which is a fundamental task in chemical synthesis. However, existing models rely on static pattern-matching paradigm, which limits their ability to perform effective logic decision-making, leading to black-box decision-making. Building on this, we propose Retro-Expert, an interpretable retrosyn-thesis framework that performs collaborative reasoning by combining the complementary reasoning strengths of Large Language Models and specialized models via reinforcement learning. It outputs natural language explanations grounded in chemical logic through three components: (1) specialized models analyze the product to construct high-quality chemical decision space, (2) LLM-driven critical reasoning to generate predictions and corresponding interpretable reasoning path, and (3) reinforcement learning optimizing interpretable decision policy. Experiments show that Retro-Expert not only surpasses both LLM-based and specialized models across different metrics but also provides expert-aligned explanations that bridge the gap between AI predictions and actionable chemical insights.

We consider the optimization of an uncertain objective over continuous and multidimensional decision spaces in problems in which we are only provided with observational data.

The Zero-shot Vision-and-Language Navigation in Continuous Environments (VLN-CE) task requires agents to navigate previously unseen 3D environments using natural language instructions, without any scene-specific training. A critical challenge in this setting lies in ensuring agents' actions align with both spatial structure and task intent over long-horizon execution. Existing methods often fail to achieve robust navigation due to a lack of structured decision-making and insufficient integration of feedback from previous actions. To address these challenges, we propose STRIDER (Instruction-Aligned Structural Decision Space Optimization), a novel framework that systematically optimizes the agent's decision space by integrating spatial layout priors and dynamic task feedback. Our approach introduces two key innovations: 1) a Structured Waypoint Generator that constrains the action space through spatial structure, and 2) a Task-Alignment Regulator that adjusts behavior based on task progress, ensuring semantic alignment throughout navigation. Extensive experiments on the R2R-CE and RxR-CE benchmarks demonstrate that STRIDER significantly outperforms strong SOT A across key metrics; in particular, it improves Success Rate (SR) from 29% to 35%, a relative gain of 20.7%. Such results highlight the importance of spatially constrained decision-making and feedback-guided execution in improving navigation fidelity for zero-shot VLN-CE.

We study \emph{online episodic Constrained Markov Decision Processes} (CMDPs) under both stochastic and adversarial constraints. We provide a novel algorithm whose guarantees greatly improve those of the state-of-the-art best-of-both-worlds algorithm introduced by Stradi et al. (2025). In the stochastic regime, \emph{i.e.}, when the constraints are sampled from fixed but unknown distributions, our method achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret and constraint violation without relying on Slater's condition, thereby handling settings where no strictly feasible solution exists. Moreover, we provide guarantees on the stronger notion of \emph{positive} constraint violation, which does not allow to recover from large violation in the early episodes by playing strictly safe policies. In the adversarial regime, \emph{i.e.}, when the constraints may change arbitrarily between episodes, our algorithm ensures sublinear constraint violation without Slater's condition, and achieves sublinear $α$-regret with respect to the \emph{unconstrained} optimum, where $α$ is a suitably defined multiplicative approximation factor. We further validate our results through synthetic experiments, showing the practical effectiveness of our algorithm.