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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. 

Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate hand-crafted acquisition functions and surrogate models for the underlying function, and often operate in a myopic manner. In this paper, we propose a novel direct regret optimization approach that jointly learns the optimal model and non-myopic acquisition by distilling from a set of candidate models and acquisitions, and explicitly targets minimizing the multi-step regret. Our framework leverages an ensemble of Gaussian Processes (GPs) with varying hyperparameters to generate simulated BO trajectories, each guided by an acquisition function chosen from a pool of conventional choices, until a Bayesian early stop criterion is met. These simulated trajectories, capturing multi-step exploration strategies, are used to train an end-to-end decision transformer that directly learns to select next query points aimed at improving the ultimate objective. We further adopt a dense training–sparse learning paradigm: The decision transformer is trained offline with abundant simulated data sampled from ensemble GPs and acquisitions, while a limited number of real evaluations refine the GPs online. Experimental results on synthetic and real-world benchmarks suggest that our method consistently outperforms BO baselines, achieving lower simple regret and demonstrating more robust exploration in high-dimensional or noisy settings. 

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. 

Transition metal dichalcogenide (TMD) twisted homobilayers have been established as an ideal platform for studying strong correlation phenomena, as exemplified by the recent discovery of fractional Chern insulator (FCI) states in twisted MoTe21–4 and Chern insulators (CI)5 and unconventional superconductivity6,7 in twisted WSe2. In these systems, nontrivial topology in the strongly layer-hybridized regime can arise from a spatial patterning of interlayer tunneling amplitudes and layer-dependent potentials that yields a lattice of layer skyrmions. Here we report the direct observation of skyrmion textures in the layer degree of freedom of Rhombohedralstacked (R-stacked) twisted WSe2 homobilayers. This observation is based on scanning tunneling spectroscopy that separately resolves the G-valley and K-valley moiré electronic states. We show that G-valley states are subjected to a moiré potential with an amplitude of ~ 120 meV. At ~150 meV above the G-valley, the K-valley states are subjected to a weaker moiré potential of ~30 meV. Most significantly, we reveal opposite layer polarization of the K-valley at the MX and XM sites within the moiré unit cell, confirming the theoretically predicted skyrmion layer-texture. The dI/dV mappings allow the parameters that enter the continuum model for the description of moiré bands in twisted TMD bilayers to be determined experimentally, further establishing a direct correlation between the shape of LDOS profile in real space and topology of topmost moiré band. 

Quasicrystals are characterized by atomic arrangements possessing long-range order without periodicity. Van der Waals (vdW) bilayers provide a unique opportunity to controllably vary atomic alignment between two layers from a periodic moir´e crystal to an aperiodic quasicrystal. Here, we reveal a remarkable consequence of the unique atomic arrangement in a dodecagonal WSe2 quasicrystal: the K and Q valleys in separate layers are brought arbitrarily close in momentum space via higher-order Umklapp scatterings. A modest perpendicular electric field is sufficient to induce strong interlayer K − Q hybridization, manifested as a new hybrid excitonic doublet. Concurrently, we observe the disappearance of the trion resonance and attribute it to quasicrystal potential driven localization. Our findings highlight the remarkable attribute of incommensurate systems to bring any pair of momenta into close proximity, thereby introducing a novel aspect to valley engineering. 

We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to improve upon the traditional worst-case run-time guarantees. Our contributions are the following: (i) We give a faster algorithm for minimum-weight bipartite matching via learned duals, improving the recent result by Dinitz, Im, Lavastida, Moseley and Vassilvitskii (NeurIPS, 2021); (ii) We extend the learned dual approach to the single-source shortest path problem (with negative edge lengths), achieving an almost linear runtime given sufficiently accurate predictions which improves upon the classic fastest algorithm due to Goldberg (SIAM J. Comput., 1995); (iii) We provide a general reduction-based framework for learning-based graph algorithms, leading to new algorithms for degree-constrained subgraph and minimum-cost 0-1 flow, based on reductions to bipartite matching and the shortest path problem. Finally, we give a set of general learnability theorems, showing that the predictions required by our algorithms can be efficiently learned in a PAC fashion