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Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common scenario in real-world applications such as the design of medical therapies, industrial process optimization, and hyperparameter optimization. One popular approach to handle these complex scenarios is Bayesian Optimization (BO). However, when it comes to the theoretical understanding of constrained Bayesian optimization (CBO), the existing framework often relies on heuristics, approximations, or relaxation of objectives and, therefore, lacks the same level of theoretical guarantees as in canonical BO. In this paper, we exclude the boundary candidates that could be compromised by noise perturbation and aim to find the interior optimum of the black-box-constrained objective. We rely on the insight that optimizing the objective and learning the constraints can both help identify the high-confidence regions of interest (ROI) that potentially contain the interior optimum. We propose an efficient CBO framework that intersects the ROIs identified from each aspect on a discretized search space to determine the general ROI. Then, on the ROI, we optimize the acquisition functions, balancing the learning of the constraints and the optimization of the objective. We showcase the efficiency and robustness of our proposed CBO framework through the high probability regret bounds for the algorithm and extensive empirical evidence. 

Online reinforcement learning (RL) enhances policies through direct interactions with the environment, but faces challenges related to sample efficiency. In contrast, offline RL leverages extensive pre-collected data to learn policies, but often produces suboptimal results due to limited data coverage. Recent efforts integrate offline and online RL in order to harness the advantages of both approaches. However, effectively combining online and offline RL remains challenging due to issues that include catastrophic forgetting, lack of robustness to data quality and limited sample efficiency in data utilization. In an effort to address these challenges, we introduce A3RL, which incorporates a novel confidence aware Active Advantage Aligned (A3) sampling strategy that dynamically prioritizes data aligned with the policy's evolving needs from both online and offline sources, optimizing policy improvement. Moreover, we provide theoretical insights into the effectiveness of our active sampling strategy and conduct diverse empirical experiments and ablation studies, demonstrating that our method outperforms competing online RL techniques that leverage offline data. Our code will be publicly available at:this https URL. 

Multi-fidelity Bayesian optimization (MFBO) is a powerful approach that utilizes low-fidelity, cost-effective sources to expedite the exploration and exploitation of a high-fidelity objective function. Existing MFBO methods with theoretical foundations either lack justification for performance improvements over single-fidelity optimization or rely on strong assumptions about the relationships between fidelity sources to construct surrogate models and direct queries to low-fidelity sources. To mitigate the dependency on cross-fidelity assumptions while maintaining the advantages of low-fidelity queries, we introduce a random sampling and partition-based MFBO framework with deep kernel learning. This framework is robust to cross-fidelity model misspecification and explicitly illustrates the benefits of low-fidelity queries. Our results demonstrate that the proposed algorithm effectively manages complex cross-fidelity relationships and efficiently optimizes the target fidelity function. 

Multi-objective Bayesian optimization has been widely adopted in scientific experiment design, including drug discovery and hyperparameter optimization. In practice, regulatory or safety concerns often impose additional thresholds on certain attributes of the experimental outcomes. Previous work has primarily focused on constrained single-objective optimization tasks or active search under constraints. The existing constrained multi-objective algorithms address the issue with heuristics and approximations, posing challenges to the analysis of the sample efficiency. We propose a novel constrained multi-objective Bayesian optimization algorithm COMBOO that balances active learning of the level-set defined on multiple unknowns with multi-objective optimization within the feasible region. We provide both theoretical analysis and empirical evidence, demonstrating the efficacy of our approach on various synthetic benchmarks and real-world applications. 

While training models and labeling data are resource-intensive, a wealth of pre-trained models and unlabeled data exists. To effectively utilize these resources, we present an approach to actively select pre-trained models while minimizing labeling costs. We frame this as an online contextual active model selection problem: At each round, the learner receives an unlabeled data point as a context. The objective is to adaptively select the best model to make a prediction while limiting label requests. To tackle this problem, we propose CAMS, a contextual active model selection algorithm that relies on two novel components: (1) a contextual model selection mechanism, which leverages context information to make informed decisions about which model is likely to perform best for a given context, and (2) an active query component, which strategically chooses when to request labels for data points, minimizing the overall labeling cost. We provide rigorous theoretical analysis for the regret and query complexity under both adversarial and stochastic settings. Furthermore, we demonstrate the effectiveness of our algorithm on a diverse collection of benchmark classification tasks. Notably, CAMS requires substantially less labeling effort (less than 10%) compared to existing methods on CIFAR10 and DRIFT benchmarks, while achieving similar or better accuracy.