potential function method

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 quantitative verification of probabilistic programs and stochastic dynamical systems, specifically aiming to rigorously infer upper bounds on the probability that a stochastic process reaches a target condition within a finite number of steps. We propose a neuro-symbolic approach: supermartingale certificates are parameterized using differentiable neural networks; training employs stochastic optimization, while formal verification leverages SMT solvers (e.g., Z3); and an counterexample-guided inductive synthesis (CEGIS) framework enables iterative refinement. To our knowledge, this is the first method to embed neural networks directly into supermartingale construction—balancing expressive power with formal verifiability—and thereby significantly improves bound tightness and reliability. Evaluated on diverse benchmarks, our computed probability bounds match or surpass those of state-of-the-art techniques. Notably, we successfully verify high-dimensional, nonlinear stochastic models that defy analysis by conventional symbolic methods.

This paper studies sublinear-time property testing under the online adversarial erasure model, where an adversary may erase up to $t$ input positions after each query, dynamically obstructing data access. We formally define this online erasure query model and establish a systematic testing framework integrating probabilistic verification, adaptive querying, and structured violation analysis. Our main contributions are: (1) proving that linearity and quadraticity are efficiently testable with tight query complexity $Theta(log t)$, matching the non-erasure setting for constant $t$; (2) demonstrating that fundamental properties such as sortedness are inherently untestable under online erasures; and (3) providing the first characterization of the intrinsic vulnerability of multiple property classes to dynamic data corruption, thereby laying a theoretical foundation for designing robust sublinear algorithms resilient to online adversarial interference.

Distributed stochastic optimization faces arbitrary computational dynamics—including hardware disconnections, time-varying compute capacity, and fluctuating processing speeds—rendering existing models inadequate for real-world deployment. Method: We propose the first general asynchronous computation model encompassing all realistic scenarios; based on it, we derive tight time-complexity lower bounds (up to constant factors) for mainstream synchronous and asynchronous methods—including Minibatch SGD, Async SGD, and Picky SGD—and prove that Rennala/Malenia SGD achieves optimal convergence. Our analysis integrates general computational dynamical modeling, information-theoretic lower-bound derivation, and stochastic optimization convergence theory. Contribution: We establish fundamental theoretical limits and design principles for system-aware optimization, providing foundational support for fault-tolerant, robust distributed learning. The results unify treatment of heterogeneous, unreliable, and dynamic execution environments while delivering precise complexity characterizations grounded in both system behavior and statistical learning theory.

This work addresses the formal robustness verification problem for Binary Neural Networks (BNNs) under ℓ∞- and ℓ²-norm adversarial perturbations. Unlike conventional NP-hard approaches based on Satisfiability Modulo Theories (SMT) or Mixed-Integer Linear Programming (MILP), we propose a novel, scalable, and numerically stable verification method. Our approach is the first to integrate sparse polynomial optimization with first-order semidefinite programming (SDP) relaxation, constructing tight continuous relaxations over the input space. This formulation substantially mitigates numerical instability and overcomes the scalability limitations of existing verifiers. Experimental evaluation on standard BNN architectures demonstrates that our method enables large-scale formal adversarial robustness verification, achieving superior efficiency and scalability compared to state-of-the-art techniques. The framework establishes a new paradigm for rigorous safety assessment of BNNs.

This work investigates adversarial binary hypothesis testing under memory constraints, where an adversary dynamically selects distributions based on past samples and the system’s current state. The detector is modeled as a time-invariant stochastic finite-state machine (FSM) with S internal states. By integrating minimax analysis with information-theoretic techniques, the study establishes matching upper and lower bounds—tight in a canonical class of problems—on the minimax error probability as a function of the number of states S. These bounds reveal an exponential decay of the error probability with S, precisely characterizing the fundamental trade-off between available memory resources and achievable detection performance.

This study addresses the weighted task scheduling problem under an adversarial model with a testing mechanism, where each task may either be executed directly or first tested to reveal a potentially shorter processing time, with the objective of minimizing total weighted completion time. For both single-machine and identical parallel machine settings, the work presents the first constant-competitive online algorithms that handle task-dependent weights, significantly improving upon existing results—even advancing the known upper bounds for the unweighted case. Building on list-scheduling strategies, the authors design deterministic and randomized algorithms achieving competitive ratios of 2.3166 and 2.1523 on a single machine, and 2.7763 and 2.5110 in the parallel setting, respectively.

This work addresses the long-standing lack of efficient value iteration algorithms for the quantitative analysis of stochastic parity games. We propose the first bounded value iteration algorithm that introduces value iteration to the quantitative solution of this problem, circumventing the high computational cost associated with traditional strategy iteration. Our approach leverages a lattice-theoretic characterization of winning probabilities and exploits structural properties of states from which almost-sure victory is achievable under parity objectives, integrating techniques from probabilistic model checking and game-theoretic analysis. We rigorously establish the correctness and convergence of the algorithm, thereby offering a more efficient and scalable method for the quantitative analysis of stochastic parity games.

This work addresses the online problem of chasing sets of size at most $k$ in metric spaces—equivalently, layered graph traversal with width $k$. By generalizing the classical doubling strategy, it presents the first deterministic online algorithm achieving an $O(2^k)$ competitive ratio against adaptive adversaries. The paper establishes the tight deterministic competitive ratio for this problem as $\Theta(2^k)$, demonstrates that the generalized Work Function Algorithm is suboptimal in this setting, and introduces a novel recursive lower-bound construction $D_k$. Notably, matching upper and lower bounds are provided for the case $k=3$, leading to improved bounds for related problems such as distributed asynchronous tree exploration and the $k$-taxi problem.

This work addresses the online linear aggregation problem with delay, aiming to balance algorithmic performance both with and without access to predictions. It proposes the first learning-augmented online algorithms—both deterministic and randomized—with rigorous theoretical guarantees. The deterministic algorithm achieves a robustness bound of $(4/\lambda + 1/\lambda^2)$ and a consistency bound of $(4+\lambda)$. The randomized algorithm attains a competitive ratio of $(e+1)$ against an oblivious adversary, surpassing the known lower bound for deterministic algorithms and improving the previous lower bound for randomized algorithms to $e$. The efficacy of the proposed methods is substantiated through comprehensive theoretical analysis and numerical experiments.