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Retailers can learn customer preferences by experimenting with different assortments. However, the cost of each experiment and the operational burden of repeatedly changing product offerings can make extensive experimentation impractical. We study how much a retailer can improve its final assortment decision using customer observations from one (or a very small number of) fixed experimental assortments. We consider the multinomial logit model, where product revenues are known but customer preferences are unknown. In this setting, we jointly design the experimental assortment and the rule for selecting a final assortment from observed customer choices to minimize worst-case regret: the expected revenue loss of the final assortment relative to an optimal assortment under the true preferences, maximized over possible customer preferences. We first characterize exactly the minimax regret and an optimal assortment when no experimentation is possible. We then show, surprisingly, that offering a single experimental assortment to just one customer can already substantially reduce regret, depending on how the products' revenues compare. We derive the exact minimax regret and an optimal experimental policy in this setting. When a single fixed experimental assortment is offered to many customers, we give a geometric characterization of the limiting minimax regret and construct an asymptotically optimal policy. Depending on product revenues, this single experiment can yield no improvement over no experimentation or nearly complete regret reduction. Finally, we extend our analysis to multiple experimental assortments chosen in advance, characterizing the limiting minimax regret, constructing asymptotically optimal policies, and identifying which collections of assortments allow worst-case regret to vanish as the number of customer observations grows.

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a simulation working directly with the nonlinear complementarity equations. Using a two-stage quantum eigenpath traversal schedule, this approach yields an algorithm for solving linear optimization problems involving $m$ constraints and $n$ variables to $\varepsilon$-optimality using $\widetilde{O}\!\left((m+n)^{3/2}\,\varepsilon^{-1}+(m+n)^{1/2}\,\varepsilon^{-3/2}\right)$ queries to an oracle that evaluates a potential function. In the standard gate model (i.e., without access to quantum RAM), our algorithm can obtain $\varepsilon$-precise solutions to LO problems using at most $$\widetilde{O}\!\left(\left[\frac{(m+n)^{3/2}}{\varepsilon} + \frac{(m+n)^{1/2}}{\varepsilon^{3/2}}\right] \cdot \mathrm{nnz}(A)\right)$$ elementary gates, where $\mathrm{nnz}(A)$ is the total number of non-zero elements found in the constraint matrix.

We study a constrained sequential decision problem for detecting regions of interest from noisy online measurements collected by a team of energy-constrained mobile sensors. The sensor motion is restricted to a precomputed set of feasible paths that satisfy mobility constraints, limited available energy by requiring return to charging stations, and avoidance of known obstacles. We cast the resulting active path selection as a multi-armed bandit problem and propose an iterative search algorithm that adaptively assigns paths using confidence bounds computed from the collected data. We also propose a graph-based method to construct low-cardinality path covers under the team's constraints. We establish finite-time and anytime probabilistic correctness guarantees for the proposed algorithm, derive non-asymptotic upper bounds on the times required to detect all regions of interest and to label all nodes, and show that these bounds match algorithm-independent lower bounds up to constant factors for a broad class of problem instances. Using numerical simulations, we illustrate the behavior of the proposed approach and the effect of path redundancy and team size on search performance.

Automated mechanism design has enabled the learning of complex auction mechanisms using neural networks. However, designing non-truthful auctions remains challenging because bidders' equilibrium strategies depend on the auction mechanism and thus evolve as the mechanism is optimized. In this work, we formulate auction design as a Stackelberg game with multiple strategic followers and develop a fully first-order algorithm for revenue optimization in non-truthful auctions. We establish non-asymptotic guarantees for hypergradient approximation and show that, under standard smoothness and strong-monotonicity assumptions, our method reaches an $O(ε)$-stationary point using $\tilde{\mathcal{O}}(ε^{-2})$ first-order oracle calls. Experiments on symmetric and asymmetric single-item auctions, as well as multi-item auctions, show that our method converges faster than second- and zeroth-order baselines and scales better as the number of bidders increases. Our method also discovers auctions that achieve revenue close to truthful baselines. These results provide a scalable framework for automated mechanism design beyond truthful auctions.

We consider the problem of finite-sample identification of an unknown LTI system from a finite hypothesis class. In contrast to existing results that assume the hypothesis class contains the true system, we consider the misspecified setting, where the true system does not belong to the hypothesis class. We first characterize the resulting estimation target and its dependence on the data-generation scheme. We then establish a finite-sample lower bound on the failure probability that any identification algorithm must incur. Finally, we analyze the robustness of an existing exponential weighting-based identification algorithm to the misspecification and derive a finite-sample upper bound on its failure probability. Our results illustrate when using a misspecified finite hypothesis class can provide an advantage over identification without prior knowledge of the candidate systems.

In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA). Our results provide the first federated Gaussian approximations for LSA that explicitly capture communication-computation trade-offs and heterogeneity-aware error terms, quantifying the effects of local step size, number of local updates, and heterogeneity on convergence rates. We present results for both (i) constant step size regime and (ii) decreasing step size with an increasing number of local iterations, recovering the recent rates of Bonnerjee et al. [2025] as a special case. As a primary application of our results, we develop an online multiplier bootstrap procedure for inference on the last iterate, which avoids explicit estimation of the asymptotic covariance matrix, and obtain non-asymptotic validity guarantees for this procedure.