non-adaptive measurement design

This paper addresses the problem of hypothesis testing for policy values in discounted Markov decision processes (MDPs): given a fixed confidence level, determine with minimal samples whether a given policy’s value exceeds a specified threshold. To overcome the computational intractability of conventional non-convex lower-bound optimization, we reformulate the problem as a policy optimization task subject to convex constraints—revealing its equivalence to policy gradient optimization in an inverse MDP. This unifies statistical optimality with computational feasibility. Based on this insight, we propose the first pure-exploration policy testing algorithm that achieves instance-dependent lower-bound matching and admits efficient implementation. Numerical experiments demonstrate that our algorithm significantly outperforms existing baselines in sample efficiency.

This work investigates the sample complexity of testing and learning $n$-qubit stabilizer states under a coherence-preserving quantum memory constraint that allows only $k$ qubits to be stored coherently. By integrating a new upper bound for the hidden shift problem, an average-case lower bound on likelihood ratios derived from combinatorial structures of the random orthogonal group, and a non-adaptive measurement framework, the study establishes—for the first time—that testing and learning complexities coincide under this memory limitation: testing requires $\Theta(n - k)$ samples, while non-adaptive learning demands $\Theta(n^2 / k)$ samples. Notably, even when $k = 0.99n$, constant-sample testing remains impossible; for $k = cn$ with $0 < c < 1$, both tasks require $\Theta(n)$ samples, revealing the fundamental role of quantum memory resources in the efficiency of quantum state identification.

To address the challenge of dynamically adapting sample size to risk level (i.e., constraint violation probability) in repeated scenario-based optimization, this paper proposes an online learning method for optimal sample size selection. The method leverages historical scenario solutions and empirically observed violation probabilities to estimate the risk distribution function in real time, thereby establishing a nonlinear mapping between sample size and risk. It is the first approach to achieve online, adaptive estimation of the optimal sample size under non-fixed computational complexity, nonconvex constraints, and time-varying distributions—overcoming the reliance of conventional scenario optimization on static problem structures—and provides theoretical guarantees of convergence. Experiments demonstrate significant improvements in both risk control accuracy and computational efficiency across diverse challenging scenarios, validating its applicability to repetitive decision-making tasks such as power system dispatch and financial risk management.

This paper addresses first-order optimization under nonlinear constraints—including nonconvex feasible sets—by proposing a novel accelerated algorithm grounded in nonsmooth dynamical systems. Methodologically, it models constraints in the **velocity space**, rather than the conventional position space, yielding sparse, local, and convex approximations of the feasible set and eliminating the need for expensive global projections at each iteration. Theoretically, the algorithm converges to stable points under nonconvex objectives and nonconvex constraints; under convexity, it achieves optimal acceleration rates in both continuous- and discrete-time settings. Its computational complexity scales nearly linearly with problem dimension and constraint count. Empirically, the method efficiently solves ℓ^p (p < 1) nonconvex regularized problems in compressed sensing and sparse regression: at p = 1, it matches state-of-the-art performance and substantially outperforms existing approaches.

This work addresses the challenge of implicit constraints—manifested as evaluation failures—arising from unreliable physics-based simulations in system architecture optimization. To tackle this, we propose a surrogate modeling framework that integrates probabilistic feasibility prediction with Bayesian optimization. Methodologically, we introduce a novel hybrid discrete Gaussian process to model the Probability of Validity (PoV), coupled with an interior-point selection strategy based on a minimum PoV threshold; the framework natively supports hierarchical design variables and multi-objective optimization. Our approach achieves the first successful solution for a jet engine architecture optimization task with a 50% simulation failure rate. Across multiple synthetic benchmarks and real-world case studies, it significantly improves convergence robustness and optimization success rate. The implementation is publicly available as the SBArchOpt Python library.

This work addresses optimization problems with convex constraints whose intersection is difficult to project onto, covering both strongly convex smooth and general nonsmooth convex settings. The authors propose a novel algorithm that integrates stochastic feasibility methods with (sub)gradient descent, wherein each iteration randomly samples a subset of constraints and employs an adaptive Polyak stepsize that requires no prior knowledge of problem parameters, complemented by iterate averaging. Theoretical analysis establishes linear convergence under strong convexity and a worst-case rate of $O(1/\sqrt{T})$ for general convex objectives, while the infeasibility measure decays geometrically almost surely. Numerical experiments on QCQP and SVM tasks demonstrate superior computational efficiency over existing methods, and under specific sampling strategies, the algorithm achieves optimal convergence rates.

This study addresses the feasibility determination problem under subjective probability constraints within a finite set of alternative systems. The authors propose a statistical inference method that operates directly on Bernoulli simulation outputs, uniquely integrating multi-threshold subjective constraints with Bernoulli observations without relying on normal approximations. To handle extreme scenarios—such as when all systems are feasible or none are—the method incorporates two heuristic strategies that dynamically adjust thresholds during execution. The resulting batch-mean-independent testing algorithm maintains rigorous statistical validity while significantly outperforming existing approaches designed for normally distributed data. Empirical experiments demonstrate the method’s computational efficiency and robust adaptability across diverse problem settings.

This study addresses the exploration–exploitation trade-off in sample size determination for test-and-roll experiments over a finite population, proposing a welfare-oriented approach that requires no prior information. The method introduces a worst-case marginal benefit (WMB) criterion, which overcomes the shortcomings of traditional minimax regret by comparing the worst-case marginal gain from adding a matched pair of observations against its marginal exploration cost. Leveraging Gaussian approximations for Bernoulli outcomes and building on the known-variance Gaussian model, theoretical analysis shows that—excluding pathological cases—the optimal experiment size is approximately one-third of the total population. This “one-third rule” offers practitioners a simple, robust, and prior-free guideline for experimental design.

This work addresses the challenge of risk prediction when acquiring true outcomes is prohibitively expensive, allowing labels for only a subset of samples. The authors propose a surrogate-assisted optimal sampling framework that, under a fixed annotation budget, leverages covariates, surrogate variables, and an initial estimator to construct a sampling strategy minimizing the expected out-of-sample cross-entropy loss. Coupled with an inverse probability weighted cross-entropy estimator for model training, this approach achieves—without requiring access to true responses during design—theoretically optimal sampling. It uniquely guarantees predictive optimality, robustness to surrogate misspecification, and stability in settings with rare outcomes. Both theoretical analysis and empirical experiments demonstrate that the method significantly outperforms existing approaches, particularly when the surrogate is imperfect or the event of interest is rare.