learning-augmented algorithms

This paper addresses online algorithm design under distributional predictions—probabilistic forecasts provided by experts or historical data—focusing on two classical problems: prophet inequalities and stochastic arrival metric matching. Methodologically, it establishes the first systematic robust competitive analysis framework for distributional predictions, introducing a novel algorithmic paradigm based on threshold policies and prediction calibration. Theoretical contributions include: (i) breaking the classical 1/2 barrier in prophet inequalities to achieve a competitive ratio of max{1/2 − η − o(1), 1/e}; and (ii) attaining zero regret (i.e., optimal cost) under perfect predictions for metric matching, with the competitive ratio smoothly degrading to the optimal no-prediction benchmark as prediction quality deteriorates. The approach integrates probabilistic analysis, competitive analysis, and stochastic matching modeling, significantly enhancing the robustness and adaptivity of prediction-driven online decision-making.

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 investigates how to integrate machine learning predictions into exact exponential-time algorithms to surpass worst-case running time lower bounds for NP-hard subset selection problems. We propose the first learning-augmented exact exponential algorithm framework, which achieves substantial search space reduction using only weak predictors—such as those slightly better than random guessing or satisfying pairwise independence. Notably, our approach operates without prior knowledge of prediction accuracy, rendering the assumptions more realistic, and provides theoretical guarantees that the running time improvement smoothly correlates with prediction quality. Crucially, even when predictions are of low fidelity, the method still ensures a provable reduction in the effective search space.

This paper identifies that algorithmic recommendations not only update decision-makers’ beliefs but also reshape their preferences by establishing themselves as default anchors—inducing “recommendation-dependent preferences” that lead to excessive compliance and Pareto inefficiency. To address this, we formally model this preference-shaping mechanism and develop a behavioral game-theoretic framework integrating Bayesian belief updating and counterfactual evaluation, proving that standard recommendation mechanisms reduce social welfare under preference dependence. We then propose a preference-aware recommendation calibration framework, wherein recommendation intensity is endogenously regulated via mechanism design. Experiments in judicial and medical simulation settings demonstrate that our calibration algorithm significantly reduces excessive compliance while improving decision efficiency and social welfare. Our core contributions are: (i) the first formal identification and modeling of algorithms’ preference-shaping effect, and (ii) the first falsifiable, implementable calibration scheme for mitigating such effects.

This paper addresses the challenge of verifying trustworthiness in probabilistic programs. Method: We propose the first computational framework that formally defines “trust” as statistical consistency between observed output frequencies and a target probability distribution. Our approach introduces an extended typed λ-calculus featuring runtime experiment operators and a static confidence-type system, enabling joint verification of dynamic sampling and distributional compliance. We establish its computability and adherence to Kolmogorov’s axioms through rigorous probabilistic semantics, along with formal proofs of progress and termination. Contribution/Results: This work achieves the first statically verifiable notion of probabilistic consistency, unifying semantic correctness with statistical reliability guarantees. It provides a theoretically sound and practically implementable foundation for trust verification in probabilistic computation.

This work addresses a critical limitation of traditional counterfactual explanations, which focus solely on flipping prediction labels while neglecting model confidence and robustness—rendering them vulnerable to perturbations in high-stakes scenarios. To overcome this, the authors propose TRUST, a novel framework that explicitly incorporates user-specified target confidence directly into the counterfactual generation process. By leveraging the interpretable clause structure of Probabilistic Tsetlin Machines (PTMs) and integrating Bayesian optimization, TRUST jointly minimizes input perturbation cost while optimizing both prediction confidence and robustness. The method achieves this by explicitly linking confidence to the stability of rule activation. Empirical results demonstrate that TRUST consistently yields highly robust counterfactuals with low recourse costs across multiple datasets; for instance, on the Haberman dataset, it attains a confidence level of 0.92 with an L2 distance of merely 0.10.

This work addresses the challenge of ensuring numerical stability, computational correctness, and physical consistency in high-stakes or scientific AI applications, where traditional post-training validation falls short. The authors propose embedding algebraic structural constraints directly into the model design phase to enable decidable correctness guarantees. Their key innovation lies in the first integration of Hindley-Milner type inference over finitely generated Abelian groups with a computable restriction of Solomonoff’s universal prior, yielding information-theoretically optimal hypotheses. This framework further combines dimensional type systems, program hypergraphs, graded Clifford algebraic inference, forward coeffect analysis, and exact posit accumulation to preserve model invariants while eliminating the cumulative computational overhead inherent in existing reliability approaches across deployment, inter-layer propagation, and inference stages.

This work addresses the longstanding challenge of reconciling theoretical correctness with practical efficiency by introducing Algorithmist, a multi-agent autonomous research system built upon GitHub Copilot. Through an iterative research-review cycle, Algorithmist collaboratively performs algorithm design, formal verification, proof-guided code generation, and consistency validation. The system establishes a scalable paradigm for provably correct algorithm synthesis by integrating large language models, structured natural-language proof representations, and formal verification techniques to generate algorithms tailored to specific datasets and deployment scenarios. In applications to privacy-preserving data analysis and clustering tasks, Algorithmist automatically produces novel algorithms that simultaneously offer rigorous theoretical guarantees and strong empirical performance, uncovers previously overlooked proof flaws in existing work, and achieves state-of-the-art results in several settings.

This study addresses sequential decision-making in humans concerning persistence versus abandonment, and investigates phenomena such as pessimism traps and insufficient ambition arising from behavioral biases and social influence in social cognition. By constructing an enhanced multi-armed bandit model, the work introduces data-driven algorithmic design into sequential decision-making for the first time and provides a formal characterization of pessimism traps. Theoretical analysis yields nearly tight upper and lower bounds on sample complexity under general conditions, demonstrating that polynomially many samples suffice to learn near-optimal policies. Furthermore, the paper proposes a sustainable community intervention mechanism that effectively disrupts pessimism traps, thereby bridging abstract theories in social epistemology with the complexities of real-world decision-making.