locally adaptive budgeting

This work addresses the challenge of maximizing end-to-end success probability in structured agent workflows under hard constraints on budget and deadline. The authors propose Monte Carlo Combinatorial Planning (MCPP), a lightweight closed-loop planner that dynamically replans during execution in response to observations. MCPP employs a finite-horizon stochastic online allocation model with parallel sampling and leverages Monte Carlo simulation to estimate, in real time, the probability of successful task completion under the given constraints. Experimental results demonstrate that MCPP significantly outperforms strong baseline methods on the CodeFlow and ProofFlow benchmarks, consistently achieving higher task completion rates across diverse budget–deadline configurations. These findings validate MCPP’s effectiveness and robustness in resource-constrained scenarios.

This work investigates the trade-off between memory and computation under a fixed online computational budget, specifically quantifying the amount of offline storage required to achieve a target accuracy. The authors propose a semi-amortized parameter optimization framework that stores a limited set of pre-solved instances offline and, at test time, retrieves the most relevant one to warm-start K steps of projected gradient descent. For smooth convex problems, they establish matching upper and lower bounds on memory complexity in the strongly convex setting, revealing a phase transition phenomenon: under β-growth conditions, the benefit of additional memory vanishes once K exceeds a certain threshold. A general framework is provided to quantify the memory cost necessary for acceleration. The theoretical findings are validated through parametric ridge regression experiments, accurately characterizing the interplay among memory, computation, and solution accuracy.

In index tuning, limited optimization budgets are inefficiently allocated to numerous “what-if” optimizer calls for query-configuration pairs (QCPs) whose costs can be accurately estimated via cost derivation, leading to budget waste and suboptimal index configurations. This paper proposes Wii, the first framework to dynamically reallocate the budget based on cost derivation accuracy. Wii employs a lightweight QCP importance assessment to identify and skip derivable “what-if” calls, redirecting saved resources toward high-uncertainty, high-impact QCPs. Designed as a plug-and-play module, Wii seamlessly integrates with mainstream enumeration algorithms. Evaluated on industrial benchmarks and real-world workloads, Wii significantly reduces redundant “what-if” calls and improves the performance of the resulting index configurations by 23%–41%.

This work addresses the lack of a unified methodology in competitive analysis of online algorithms by proposing a posterior matching principle grounded in a minimax perspective. Leveraging Yao’s principle, it reframes worst-case competitive analysis as a Bayesian online design problem with an arbitrary correlated prior, selecting at each step the feasible action closest to the posterior expected optimum. The framework integrates Bayesian inference, posterior process tracking, martingale analysis, and randomized rounding, establishing a connection between information theory and competitive ratios via vector martingale inequalities. It achieves or surpasses the best-known competitive ratios for fractional problems—including set cover, load balancing, matching, and generalized resource allocation—and provides, for the first time, theoretical guarantees for randomized algorithms on integer problems such as weighted paging, star-metric metrical task systems, and ski rental.

This paper studies online interval scheduling and edge-disjoint path allocation on general graphs under imperfect predictions. Given a dynamically arriving sequence of intervals, the objective is to maximize the number of mutually non-overlapping intervals; this is generalized to path allocation on arbitrary graphs. We establish, for the first time, a tight characterization linking prediction error to competitive ratio. Our method integrates online algorithm design, error-sensitive competitive analysis, and empirical evaluation on real-world workloads. We propose an asymptotically optimal trade-off framework that ensures consistency—achieving near-optimal performance when predictions are accurate—and robustness—degrading gracefully to the classical competitive bound under severe prediction errors. We derive matching upper and lower bounds on the error-dependent competitive ratio. Both theoretical guarantees and empirical results demonstrate strong alignment, significantly enhancing the rigor and practicality of learning-augmented online algorithms.

研究在线分配问题，通过少量样本在对抗顺序下实现资源的有效分配或负载均衡。提出一种通用框架将随机顺序模型算法转换为适用于更复杂采样模型的算法。

Web agents have achieved significant success in automating complex internet tasks but deploying them in real-world environments requires continuous online adaptation. Given that deploying powerful proprietary models remains commercially cost-prohibitive, practitioners must rely on lightweight local models that evolve post-deployment via online teaching from a stronger teacher. However, standard interactive feedback imposes prohibitive costs. We show that conventional trajectory-level preference optimization wastes budget on both unresolvable episodes and redundant execution turns. To resolve these inefficiencies, we propose \textbf{Score-Guided Online Teaching with Budgeted Trajectory Trimming}, a budget-aware framework that systematically orchestrates \textbf{when} and \textbf{what} to teach. Specifically, our framework integrates a solvability-aware teacher gate to dictate \textbf{when} to query the teacher model and a score-guided turn selection mechanism to decide \textbf{what} informative turns to retain. Extensive experiments on MiniWoB and TimeWarp demonstrate that our method achieves comparable first-pass success while reducing teacher calls by 22.6\% and student training compute by 52.1\% on average. Our code is available at https://github.com/zjw131f1fc/budgeted-online-teaching.

This work addresses the limitations of existing stepwise caching methods for diffusion models, which rely on heuristic thresholds and struggle to jointly optimize generation quality and inference latency under a fixed computational budget. To overcome this, the authors propose BudCache, a novel framework that shifts cache decisions from error-threshold-driven heuristics to explicit budget-constrained optimization. BudCache performs offline combinatorial optimization to identify the optimal caching strategy, thereby eliminating online overhead. The approach efficiently solves this optimization problem by integrating simulated annealing with deterministic hill climbing and further introduces a cache-aware time discretization alignment mechanism to mitigate trajectory mismatch. Experiments on FLUX.1-dev and Wan2.1 demonstrate that BudCache significantly outperforms current heuristic caching baselines in generation quality under identical inference budgets.

本文针对多模型语言服务中的请求路由问题，提出了一种名为Drift-Aware Sparse Routing (DRS)的方法，通过稀疏上下文和动态调整资源估计来优化计算、延迟、内存或成本的预算约束。

This work addresses the sequential estimation of function values in slowly varying sequences by introducing a general adaptive framework applicable to a wide range of linear and nonlinear functions over vector spaces. The method reuses historical query information and incorporates a local adaptive budget allocation mechanism that dynamically adjusts computational resources based on real-time variation magnitudes. It achieves, for the first time, a path-length–type cost bound of \(O(\sum \alpha_i)\), improving upon prior fixed-budget approaches that rely on worst-case assumptions about individual \(\alpha_i\). In certain settings, the variation magnitude can be estimated online with negligible overhead. Applied to tasks such as matrix powers, spectral density estimation, Monte Carlo integration, and PDE boundary value problems, the framework substantially reduces computational costs, with both theoretical analysis and empirical results demonstrating its pronounced efficiency advantage when stable sequences experience occasional abrupt changes.