cost-aware information-directed selection

This paper addresses the exploration-exploitation trade-off in multi-armed bandits by proposing Information-Directed Sampling (IDS), a strategy that jointly optimizes immediate regret and information gain. It extends IDS to the discounted infinite-horizon setting for the first time, introducing a novel information measure and a tunable information-regret trade-off parameter. In a two-state Bernoulli bandit environment, the authors provide rigorous finite-time analysis of IDS’s suboptimality gap relative to the Bayesian optimal policy: it achieves bounded cumulative regret in the symmetric arms setting and attains logarithmic regret—matching the asymptotic theoretical lower bound—in the single fair-coin setting. The analysis integrates information-theoretic tools (KL divergence, mutual information), Bayesian reinforcement learning (discounted MDPs, posterior updates), and statistical asymptotics. These results establish IDS as both theoretically optimal and practically viable, offering a new paradigm for information-driven sequential decision-making.

This paper studies sequential stochastic combinatorial optimization with costly information acquisition: it jointly optimizes solution quality and observation cost within an acyclic Markov decision process (MDP) framework, under matroid constraints and bandit-style feedback. Addressing the limitation of prior work—restricted to special cases—we propose a novel cost-allocation bound coupled with a local approximation framework, enabling lossless approximate composition of solutions for arbitrary component MDPs. Our approach transcends structural restrictions inherent in classical models such as Pandora’s Box, and unifies treatment of a broad class of variants—including the newly introduced Weighing Scale problem—yielding constant-factor optimal approximation algorithms either for maximizing expected reward or minimizing total cost.

Evaluating learning-augmented online algorithms under uncertainty remains challenging, as conventional metrics focus narrowly on worst-case prediction errors, neglecting both prediction accuracy and risk sensitivity. Method: We propose a dual-track evaluation framework grounded in decision theory, jointly incorporating distance-based prediction error quantification (deterministic aspect) and risk-sensitive modeling (stochastic aspect). By embedding decision-theoretic loss functions into online algorithm analysis, we integrate prediction error modeling with risk-controllable optimization, designing novel learning-augmented algorithms for contract scheduling and 1-max search. Contribution/Results: Our approach achieves provable robustness to prediction errors, performance guarantees with tight bounds, and explicit risk controllability. It is the first to unify prediction accuracy, worst-case robustness, and risk preference within a single theoretical framework—establishing a systematic evaluation paradigm and design principle for learning-augmented online algorithms.

This work addresses the challenge of applying traditional multi-winner voting rules in large-scale or attention-constrained settings, where eliciting complete preference rankings from voters is impractical. To overcome this limitation, the authors propose a structured-query framework for multi-winner elections that approximates an optimal committee by querying voters’ preferences over subsets of candidates within a limited budget. They formally define a cognitive cost function and axiomatic evaluation criteria, and introduce a query strategy based on recursively partitioning the candidate set. Experimental results demonstrate that this approach significantly outperforms alternative querying mechanisms across various election models and multi-winner rules—such as k-Borda—achieving high committee selection accuracy while substantially reducing the information acquisition cost.

This paper studies cost-aware sequential hypothesis testing: a decision-maker selects actions with random positive costs to identify the true hypothesis while minimizing the expected total cost, subject to an average error-rate constraint. We innovatively introduce an adjustable per-action deadline mechanism that allows action termination to cap unbounded costs. Under the ex-post cost revelation model, we prove that deadlines do not alter the optimal expected cost. In the ex-ante model—where costs are unknown at selection time—we first quantify the deadline-induced inflation in action frequency and propose the “effective equivalent cost” concept, enabling performance under stochastic costs to approach that of the constant-cost benchmark. Our methodology integrates sequential decision-making, optimal stopping, Bayesian hypothesis testing, and cost-sensitive optimization.

This paper addresses the classical secretary problem—online selection of the best candidate based solely on relative rank information. To overcome the poor adaptability of conventional fixed-threshold policies, we propose a data-responsive heuristic framework featuring sequential threshold adaptation. It integrates five tunable rules—including expected-record thresholds, adaptive bias correction, and probabilistic early-stopping—and employs two-stage relaxation with local dynamic programming approximation to enhance robustness and decision efficiency. The method synergistically combines probabilistic modeling with lightweight ensemble learning. Extensive simulations across diverse scenarios validate its efficacy. Experimental results show that the framework achieves near-optimal performance with minimal intuitive hyperparameters, consistently outperforming classical strategies in both average-case performance and stability; the ensemble variant demonstrates the highest robustness.

This paper addresses a fundamental limitation of classical priced query models—where query costs must be fully known in advance—by introducing and studying the “cost-unknown” priced query model, wherein query costs are unpredictable and revealed only upon querying. The objective is to adaptively determine a variable querying order that minimizes the total cost required to evaluate a Boolean function. Method: We establish a lower bound on the competitive ratio induced by cost uncertainty and design a universal adaptive strategy leveraging Boolean function sensitivity analysis and online competitive analysis techniques. Contribution/Results: Our strategy achieves a near-optimal competitive ratio—tight up to a constant factor—for arbitrary Boolean functions. This work bridges the theoretical gap between cost-aware and cost-agnostic query policies for the first time, significantly extending the applicability of priced query theory to settings with incomplete cost information.

This paper addresses the non-uniform sequential hypothesis testing problem: minimizing the expected total cost of identifying the true hypothesis, where actions incur heterogeneous positive costs and the average error probability is constrained to be at most δ. Recognizing that the conventional “bit-per-unit-cost” criterion leads to suboptimal performance, we propose a new design principle that maximizes the ratio of expected information gain to expected action cost—thereby preserving the optimal log(1/δ) sample complexity. Building upon the Chernoff framework, we develop an adaptive policy that explicitly couples information acquisition efficiency with action cost-effectiveness. Simulation results demonstrate that our method reduces average cost by 50% compared to the classical Chernoff strategy and by up to 90% relative to a naive “bit-per-buck” heuristic, significantly improving decision efficiency and resource utilization in heterogeneous-cost settings.

This work addresses the challenge of high-variance-induced sampling costs in index-assisted approximate query processing for ad-hoc aggregation over frequently updated flat data, where existing methods struggle to balance accuracy and low latency. To overcome this limitation, we propose a two-stage online stratified sampling framework that, for the first time, integrates stratified sampling into index-assisted online aggregation. In the first stage, samples are used simultaneously for real-time estimation and to refine the subsequent sampling strategy; the second stage performs efficient sampling based on an optimized stratification structure and Neyman allocation. We develop greedy and dynamic programming algorithms tailored to an index-aware sampling cost model to balance efficiency and accuracy. Experimental results demonstrate that our approach achieves up to 3× speedup over index-assisted uniform sampling and up to 98,708× speedup compared to traditional scan-based stratified sampling.