incremental update algorithms

This work addresses the challenge in time-varying Bayesian optimization (TVBO) where the rate of change of the objective function is unknown. To this end, we propose an adaptive optimization framework that requires no prior assumptions on the change rate. Methodologically, we introduce an event-triggered mechanism that dynamically detects model mismatch and resets the Gaussian process (GP) surrogate based on a probabilistically consistent error bound; this is integrated with an upper-confidence-bound (UCB) sampling strategy for online sequential optimization. Theoretically, we are the first to employ a probabilistically consistent error bound for triggering GP model updates, and we rigorously establish a sublinear regret bound under adaptive reset conditions. Experiments on synthetic and real-world benchmarks demonstrate that our method significantly outperforms standard GP-UCB and existing TVBO variants, exhibiting strong robustness and minimal sensitivity to hyperparameter tuning.

This work addresses the problem of efficiently maintaining a breadth-first search (BFS) tree rooted at a source vertex in graphs undergoing dynamic edge updates—insertions, deletions, or a mix of both. It introduces, for the first time, predictive models into the dynamic BFS setting and proposes incrementally and decrementally updated strategies guided by prediction errors (denoted η_v, η^*_v, and η_e). The approach extends the classic Even–Shiloach (ES) tree to support batch processing and fully dynamic scenarios. In incremental and decremental settings, the algorithm achieves worst-case update times of O(η_v + η_e) and O(min{m, η^*_v + η_e}), respectively, while retaining comparable efficiency in the fully dynamic case—substantially outperforming the naive O(m) recomputation baseline.

This work addresses the challenge that small language models often fail to reliably execute multi-step, dependency-rich structured graph algorithms due to error accumulation. The authors frame algorithm execution as a closed-loop prediction task, wherein the model iteratively selects operations based on the current graph state and evaluates its overall behavior through full rollbacks. Departing from conventional step-isolated evaluation, this closed-loop rollback paradigm reveals that strong single-step prediction accuracy does not necessarily ensure stable global execution. Experimental results demonstrate that suitably adapted small models can reliably perform algorithms such as traversal and coloring, yet remain vulnerable to cumulative errors in weighted graph algorithms. These findings underscore the necessity and efficacy of the proposed closed-loop evaluation framework for assessing and improving algorithmic reasoning in language models.

This work addresses the Bayesian exploration problem where items exhibit graph-structured dependencies, aiming to adaptively probe edges under a knapsack constraint to maximize expected total reward. Vertices are independently activated with known probabilities, and probing an edge yields an immediate reward while revealing the states of its endpoints, thereby triggering Bayesian updates. The paper presents the first efficient approximation algorithm for this class of problems and extends it to a practical family of prior distributions commonly used in Bayesian active search. By integrating graphical models, Bayesian inference, and stochastic optimization techniques, the proposed method achieves a provable approximation guarantee while significantly improving empirical performance, effectively alleviating the computational bottleneck inherent in Bayesian active search.

This work breaks the long-standing deterministic lower bound on update time for dynamic maximum matching in dense graphs. Previously, all deterministic algorithms required Ω(n) amortized update time on n-vertex dense graphs. We present the first deterministic dynamic algorithm that maintains a maximal matching in Õ(n⁸⁄₉) amortized time—surpassing the linear barrier. Our approach introduces three key techniques: (1) repurposing the Edge Degree Constrained Subgraph (EDCS) to guarantee full matching of high-degree vertices, diverging from its conventional use for approximation; (2) integrating sublinear-time matching computation, random walks on directed expander graphs, and monotonic Even–Shiloach trees; and (3) designing a randomized algorithm achieving Õ(n³⁄₄) amortized time against an adaptive adversary. These advances collectively establish new state-of-the-art bounds for deterministic and randomized dynamic maximal matching in dense graphs.

This work addresses the limited adaptability of Bayesian experimental design under dynamic constraints—such as budget, cost, or physical limitations—by introducing a novel approach that integrates offline amortized inference with online multi-step lookahead planning. The method uniquely combines a pretrained amortized posterior policy with scenario-tree-based online planning to efficiently optimize sequences of experiments while respecting evolving constraints. By jointly leveraging amortized Bayesian inference, scenario tree construction, and constrained optimization, the proposed framework substantially enhances the information gain of selected experiments across diverse constrained tasks, achieving high efficiency and strong adaptability with only modest additional computational overhead.

This work addresses the instability of traditional predictive models in performative prediction settings, where deployed algorithms alter data distributions and induce feedback loops. The authors propose an unconditional reduction framework that avoids strong assumptions about how models influence data generation, leveraging randomization and martingale theory to circumvent computational barriers in existing stability analyses. By establishing a theoretical bridge between performative prediction and online learning, they prove that any no-regret algorithm converges to a mixed performative stable equilibrium—where the induced data distribution renders the model’s predictions ex post optimal. This result reveals that common algorithms such as gradient descent inherently possess stabilizing mechanisms that mitigate runaway feedback effects.

This study addresses the problem of efficiently identifying the initial state in partially observable Markov chains, particularly under passive observation and limited-efficiency constraints. To this end, the authors introduce and systematically analyze, for the first time, a novel model termed “Markov chains with support for backtracking,” which permits algorithms to strategically revert the process to prior states to accelerate learning or decision-making. The key contributions include establishing the equivalence between non-adaptive and adaptive backtracking strategies in terms of state distinguishability, and constructing a non-adaptive strategy whose query complexity exceeds that of the optimal adaptive strategy by only a polynomial factor—a gap proven to be unavoidable. The theoretical analysis integrates probability theory, information theory, and computational complexity, thereby establishing a new analytical framework for reasoning about backtracking mechanisms.

Scientific workflows often involve optimization objectives and evaluation criteria that are inherently uncertain and evolve with accumulating evidence, posing challenges for traditional Bayesian optimization methods. This work proposes the Generate-Select-Refine (GSR) framework, which uniquely integrates open-ended task discovery into the Bayesian optimization loop. Starting from user-provided seed tasks, GSR generates new tasks in a coarse-to-fine manner and employs a task acquisition function to orchestrate the optimization process, enabling alternating cycles of task discovery and refinement. The approach incurs only logarithmic regret overhead, transcending the limitations of single-task optimization. Empirical results demonstrate that GSR significantly outperforms existing large language model–based optimizers across diverse domains, including new product development, chemical process scale-up, algorithmic analysis, and patent repurposing.

This work challenges the prevailing assumption that standard acquisition functions—such as Upper Confidence Bound (UCB)—in asynchronous Bayesian optimization inherently lead to redundant queries. Through rigorous theoretical analysis and empirical evaluation, the authors demonstrate that, when intermediate posterior updates are properly accounted for, these standard acquisition functions naturally avoid excessive resampling without requiring additional diversity-enforcing mechanisms. Moreover, the study reveals that explicitly imposing diversity penalties can inadvertently induce over-exploration, degrading performance. Extensive experiments on both synthetic benchmarks and real-world tasks show that the standard approach not only matches but often surpasses the performance of more complex algorithms specifically designed for asynchronous settings, thereby questioning the necessity of specialized diversity strategies in this context.