cloud resource managers

Abstract: We revisit scheduling with obligatory testing, where each job consists of two operations: a test with an initially known time and an operation whose processing time is revealed upon completion of the job's test. We develop an iterative competitive-ratio-preserving instance-reduction method that enables us to compute exact competitive ratios directly on highly structured instances for various index rules. Our main result is a clean analysis showing that the competitive ratio of the algorithm $1$-SORT is exactly the Golden Ratio $\varphi\approx 1.618$, improving the recent best-known upper bound of $1.861$ for arbitrary testing times. We further leverage this method to obtain near-tight bounds for a simple randomized algorithm on instances with uniform testing times.

Abstract: Accurate time series forecasting (TSF) is essential for Web applications, such as traffic monitoring and online resource management. Recent advances in leveraging pre-trained large language models (LLMs) have shown promising performance in TSF. However, existing LLM-based TSF methods largely optimize the overall forecasting objective while overlooking temporal pattern imbalance (TPI), where different temporal patterns occur at highly unequal frequencies. Our empirical analysis reveals that TPI is prevalent across widely used TSF benchmarks, with substantially higher forecasting errors on less frequent patterns. To address this issue, we propose IMRouter (Imbalance-aware Temporal Pattern Routing), a novel framework that mitigates TPI-induced biases in both temporal representation learning and cross-modal alignment. Specifically, IMRouter introduces Pattern-Adaptive Temporal Representation Learning (PATR), which leverages gradient conflict and local gradient density to guide expert specialization. By penalizing incompatible expert assignments with density-aware weighting, PATR reduces the dominance of frequent optimization signals in router training. Furthermore, Routing-Guided Semantic Alignment (RGSA) transfers the pattern-specific knowledge learned by the router to cross-modal alignment through mutual information maximization, preserving distinctive temporal information across different patterns. Extensive experiments on benchmark datasets demonstrate the effectiveness of IMRouter, particularly in improving forecasting performance on less frequent temporal patterns.

Abstract: Multi-task post-training can develop domain specialists through independent reinforcement learning (RL) and consolidate their capabilities through multi-teacher on-policy distillation (MOPD). However, standard MOPD generates on-policy student responses and keeps multiple teachers online throughout consolidation, introducing substantial system costs. We view this pipeline as domain-wise exploration followed by cross-domain exploitation. Domain RL produces not only the final specialists, but also the trajectories collected throughout their training. Existing methods primarily use the former while leaving the latter underutilized. We introduce DoubleFree, which reuses these historical trajectories for rollout-free consolidation and precomputes teacher supervision for online-teacher-free student training. To understand why this works, we analyze when updates from historical trajectories can approximate on-policy distillation updates and how combining trajectories across exploration stages can better support an evolving student. DoubleFree requires only minimal changes to existing post-training frameworks. Across math, code, and instruction following on Qwen3-4B, Qwen3-8B, and SmolLM3-3B, DoubleFree achieves $2.99$-$5.75\times$ consolidation speedups and reduces GPU-hours by $80.9$-$90.1\%$, while maintaining comparable multi-domain performance.

Abstract: The asymptotic competitive ratio of online bin packing has been bracketed since 2018 by the lower bound 1.54278 of Balogh, Bekesi, Dosa, Epstein and Levin and the upper bound 1.57829 of their Advanced Harmonic algorithm. We revisit both sides with exact rational computation and prove what the computations say. On the upper bound, we rebuild the certification of Advanced Harmonic as an exact optimization over its dual parameters; with the published parameters this already certifies a ratio strictly below the published one, and re-tuning the algorithm's proportion parameters gives a certified ratio of 1.5782147437 (an exact rational), independently re-verified on all 402 scenarios. To our knowledge this is the first movement of the upper bound since 2018. On the lower bound, we prove that the 2018 adversary construction is rigid: extending it by any finite number of new batches of ordinary size (outside the window of sizes s with 2s > 1 and rational part at most 0.64819), placed anywhere, with counts depending on the observed statistics, adaptive or not, never improves the bound at any truncation level. The load-bearing fact is that the construction is volume-tight at every stop. A single window-sized batch added to the truncation-3 tree is shown by machine-verified certificates to leave its value below the published limit. A computational map covers the remaining natural extensions: unions of structural variants, two-statistic multi-batch adversaries, and three families of adaptive conditions that the paper's separation theorem allows but never uses; none improves the bound. On the algorithm side we show that the marking, bonus-item and red-sand mechanisms of Extreme Harmonic bind nowhere in Advanced Harmonic, whose bottleneck is a two-medium-item bin that no known mechanism targets. We record two corrections to commonly cited numbers.

Abstract: We argue that cooperative multi-agent reinforcement learning (MARL) should treat test-time coordination as part of the problem definition rather than a deployment artifact. Our focus is on long-horizon, centrally monitored cooperative systems such as warehouse robotics, automated storage-and-retrieval systems, and cloud-resource scheduling, where teams share a reward, operate under shifting objectives, and already run with global telemetry at deployment. The dominant paradigm in this regime, centralized training with decentralized execution (CTDE), uses global information only during training and provides no coordination channel at execution. This is sufficient when agents are weakly coupled or the environment is stationary, but it fails when the team must realign after conditions change. The limitation is structural rather than algorithmic, and more training cannot add a channel that does not exist at execution time. We call this the recoverability gap. To address it, we name the underexplored design space of intermittent test-time coordination as centralized training with mixed execution (CTME), in which a coordinator observes global state and emits high-level signals while agents act locally. CTME is not a particular learning algorithm, but a cooperative MARL problem setting that makes test-time information structure explicit. It specifies team-level information, high-level signals, and update frequency after training, with CTDE recovered as a limit case. We do not argue that CTDE is obsolete. We argue that removing the test-time channel is a modeling choice, not a necessity, and the wrong default when global telemetry is available and teams must recover from drift.

Abstract: Real-world systems often serve many objectives but can deploy only a few options, whose performance must be learned from noisy feedback. Modeling each option as an arm in a multi-objective bandit, we introduce \emph{few-for-many best-arm identification}, which seeks a small set of arms minimizing the worst weighted degradation from the objective-wise optima, rather than the best arm for every objective. We consider both known objective groups and latent groups specified only by a representative budget, and propose \textsc{GFM-Elim} and \textsc{AFM-Elim} with instance-dependent sample-complexity guarantees. For Gaussian rewards, we further derive a lower bound for the latent-group setting and show that it is asymptotically attainable with high probability by an oracle-based Track-and-Stop procedure. Our results show that sharing observations across objectives and ignoring irrelevant objective-wise distinctions can substantially reduce the sampling cost, as confirmed by experiments on synthetic and real-world tasks.

Abstract: We study the fair allocation of $m$ indivisible chores among $n$ agents in the agent-arrival model against an oblivious adversary. The chore set and the number of agents are known in advance. When agent $i$ arrives, her nonnegative additive cost function $c_i$ is revealed, and the algorithm must immediately and irrevocably assign her a subset of the unallocated chores. We focus on the notion of maximin share (MMS) and measure the fairness of the realized allocation $X$ by the ex-post MMS approximation ratio $ρ(X)$. We measure an algorithm's performance by its expected ratio, and also the guarantees that hold with high probability. For binary additive costs, we achieve an expected ex-post MMS ratio of $3/2+o(1)$, and show that every randomized online algorithm has an expected ratio of at least $3/2-o(1)$. For every $n$, the expected ratio is at most $1.755$. A variant of our algorithm guarantees an approximation ratio of $2$ with high probability, which is optimal. % For general additive costs, we present a weighted-rounding algorithm that achieves an expected ratio of $2+o(1)$, which also holds with high probability. The expected ratio is at most $2.594$ for every $n$. We also show that similar algorithms extend to additive goods, achieving a constant expected ex-post MMS ratio and guaranteeing every agent an $x$-fraction of her MMS with probability at least $1-85x^2$ for every $x\le1/15$.

Abstract: We study online scheduling of parallel jobs on $m$ identical processors to minimize maximum flow time. Each arriving job is represented by a directed acyclic graph (DAG) whose vertices are unit-time subjobs and whose edges specify precedence constraints. We consider non-clairvoyant algorithms: the DAG is not known when a job arrives, and each subjob is revealed only when it becomes ready. Agrawal, Moseley, Newman, and Pruhs (SPAA 2024) showed that First-In-First-Out (FIFO) has competitive ratio $Ω(\log m)$ even when every job is an out-tree. They also proved that FIFO is $O(\log m)$-competitive in several natural settings and asked whether this guarantee extends to general instances. More broadly, they asked whether any non-clairvoyant algorithm can be $O(1)$-competitive. We answer both questions in the negative by proving a lower bound of $Ω(\min\{m,\mathrm{OPT}\})$ for every non-clairvoyant online algorithm, where $\mathrm{OPT}$ is the maximum flow time of an optimal offline schedule. In particular, every non-clairvoyant algorithm has competitive ratio $Ω(m)$ on some instance with $\mathrm{OPT} \ge m$. The lower bound holds even when every job is an out-forest. We complement these lower bounds with an asymptotically optimal non-clairvoyant algorithm. FIFO is $O(m)$-competitive, but can have competitive ratio $Ω(m)$ even when $\mathrm{OPT}=O(1)$. For instances with small $\mathrm{OPT}$, we design a Small-Frontier-First algorithm that is $O(\mathrm{OPT})$-competitive. Combining the two algorithms yields an $O(\min\{m,\mathrm{OPT}\})$-competitive non-clairvoyant algorithm.

Abstract: We study finite-horizon online resource allocation with i.i.d. requests and an endogenous Markov state on a finite state space: each action affects the transition of the state that governs future rewards and resource consumption. In this problem, a transient fluid LP benchmark upper bounds the expected reward of every nonanticipating policy, while a stationary LP supplies randomized state-dependent controls. We assume that the stationary LP has a unique optimum and identify primal nondegeneracy and irreducibility of the optimal induced kernel as important regularity conditions in this framework. With a known request prior, we show that, under nondegeneracy and irreducibility, both frequent and infrequent re-solving attain $O(1)$ regret. However, under a degenerate optimum, irreducibility yields the sharp worst-case $Θ(\sqrt{T})$ rate for infrequent re-solving, while frequent re-solving can incur $Ω(T)$ regret. Thus, more frequent optimization can perform asymptotically worse. With an unknown request prior, we develop a three-phase U-shaped infrequent re-solving policy that coordinates learning and inventory correction with $O(\log\log T)$ LP solves. When the optimal induced kernel is irreducible and the algorithm is given the optimal target state class and a constant-cost entrance policy, it attains $O(1)$ regret under nondegeneracy and $O(\sqrt{T})$ regret under degeneracy. Without the target-class information, linear minimax regret is unavoidable. Numerical experiments further illustrate the instability of round-by-round re-solving relative to epoch-wise infrequent re-solving, show that thresholding greatly mitigates its loss, and find that infrequent schemes remain dominant under both known and estimated priors.

Abstract: We study single-sample prophet inequalities for online combinatorial allocation. Our main contribution is a general reduction from combinatorial to single-item prophet inequalities for valuation classes admitting suitable supporting prices. The reduction uses a free-disposal value to separate buyer-side combinatorial constraints from item-side supply constraints, yielding a modular framework that applies in the stronger Game of Googol model. This framework yields a $\frac{1}{6\sqrt{3}}\approx\frac{1}{10.4}$-competitive single-sample prophet inequality and a $(β_{k-1}/4)$-competitive $k$-sample prophet inequality for XOS valuations, where $β_k$ is the competitive ratio of a $k$-sample single-item prophet inequality, improving upon the work of [DKL+24]. Both results extend directly to divisible resources with capped-XOS valuations. Along the way, we obtain new results for online free disposal and an optimal single-sample prophet inequality for fractional knapsack in the Game of Googol model.

Abstract: Scheduling problems arise from repeatedly selecting one item from a set of candidates based on their states. These problems often reduce to assigning priority scores and choosing the highest-ranked item. In this work, we propose a factorized scheduling principle (FSP) framework to learn interpretable and transferable scheduling rules. The FSP framework represents system states as condition distributions and decomposes a global scheduling principle into additive univariate and pairwise components with identifiability constraints. The scheduling principle enables the framework to maintain a simple priority-based structure during deployment. This principle is learned by using a policy-based objective combined with a temporal-difference signal defined on the condition distribution. Experiments on synthetic and realistic scheduling tasks demonstrate the FSP framework's strong performance, interpretability, and zero-shot generalization across different system scales.

Abstract: In this work we initiate the study of competitive algorithms with arrival-time incentive compatibility for random-order online bipartite matching in settings where the users care only about receiving service (matched vs. unmatched) and not which offline resource serves them, while the platform's objective is to maximize total matching reward. This captures applications such as ride-sharing where the users primarily care about being matched to a ride while the platform internalizes the cost of dispatching a distant driver; dispatching homogeneous service requests to heterogeneous servers (cloud/edge routing); and assigning customer requests to a pool of providers with different flexibility (e.g., English-only vs. bilingual agents). Our main question is: \textit{Is constant-competitive matching possible for incentive-compatible, random-order edge-weighted matching on complete bipartite graphs?} Motivated by the LP-based treatment of incentive compatibility in the classical secretary problem by Buchbinder et al., we impose a constraint that the ex ante probability of selection is equalized across all arrival positions. We answer our main question in the affirmative and propose the first constant-competitive algorithm for incentive compatible edge-weighted random-order online matching on complete bipartite graphs. The competitive ratio of our algorithm is parameterized by the imbalance factor $k := n/m$ -- where $n$ and $m$ are the numbers of online and offline nodes, respectively, and $k$ is a positive integer. In particular, we obtain a competitive guarantee of the form $c_k - O(1/\sqrt{m})$ where $c_1 \approx 0.162$ and $c_k \to 0.02308\ldots$ as $k \to \infty$. We also present algorithms with strictly improved competitive ratio of $\approx 0.07 + O(1/m)$ for the binary-weighted case ($0$-$1$ rewards).

Abstract: Quantum cloud computing, delivered through the quantum-as-a-service (QaaS) model, provides access to quantum computing resources. However, applying uniform time-based pricing across fundamentally heterogeneous quantum resources significantly complicates task orchestration, particularly when addressing the tradeoff between execution costs and system performance. While heuristic methods rely on predefined scheduling rules, classical deep reinforcement learning (DRL) models may require more trainable parameters in this setting. Motivated by the potential of parameterised quantum circuits (PQCs) as compact function approximators, we propose QRLQ, a cost-delay-aware quantum cloud scheduling framework integrating PQCs with a dueling double deep Q-network (D3QN) to dynamically account for both cost and delay. Our simulation results show that QRLQ achieves lower mean cost and delay than the heuristic baselines, achieving a 5-11% lower mean cost relative to availability-based and rotation-based heuristics and reducing mean delay by 17% and 82% relative to the strongest and weakest heuristic baselines, respectively, while retaining execution fidelity within 2% of a fidelity-greedy policy. Compared with the classical DRL baseline, QRLQ achieves comparable scheduling performance while using 72% fewer trainable parameters. This work explores the feasibility of using QRL for task orchestration in quantum cloud environments and demonstrates its potential for cost-delay-aware quantum resource management.

Abstract: We study randomized algorithms for the fully online allocation of indivisible goods among $n\ge2$ agents with nonnegative additive valuations. Goods arrive one by one and must be allocated immediately and irrevocably. Nothing is known in advance except the number of agents. Since exact ex-ante envy freeness and proportionality are readily achievable, while no positive ex-post approximation is possible for the fairness notions considered here, we study the intermediate notions of high-probability fairness and expected realized fairness. Against a non-adaptive adversary, we give a randomized algorithm that achieves an $Ω(\sqrt{\log n}/\log(n/δ))$-approximation to proportionality up to one good (PROP1) with probability at least $1-δ$ for every $δ\in(0,1)$, and an expected realized PROP1 factor of $Ω(1/\sqrt{\log n})$. Compared with independent uniform allocation (Rand), these guarantees yield an $Ω(\sqrt{\log n})$ improvement under both the high-probability and expected realized criteria. For envy freeness up to any good (EFX), the success probability of any positive factor can be made arbitrarily small, even for identical valuations. Consequently, the expected realized factor of every randomized fully online algorithm is zero. For envy freeness up to one good (EF1), no randomized fully online algorithm can guarantee a positive factor with confidence exceeding $\frac{n+1}{2n}$. The expected realized EF1 guarantee is also at most $\frac{n+1}{2n}$.

Abstract: We study online allocation with convex costs (\OACC), a generalization of limited-supply models in which additional resources can be produced dynamically at convex cost. Prior work largely focuses on constructing a single algorithm that achieves strong competitive guarantees. In contrast, our main contribution is a structural characterization of the optimal design space of reserve functions (i.e., normalized pricing rules) for \OACC, yielding a family of optimal online algorithms. Using a principled dynamical-systems approach, we show that optimal online algorithms arise as solutions of a nonlinear eigenvalue problem: the optimal competitive ratio corresponds to the dominant eigenvalue, and the associated eigenfunction determines the optimal reserve function. This perspective establishes the existence of infinitely many optimal designs attaining the best possible competitive ratio, thereby unifying and generalizing a broad class of prior algorithms. Beyond unification, our characterization uncovers new structural phenomena, including the ability to flexibly mix dynamic and static pricing without loss of optimality and the construction of universally competitive algorithms under unknown or stochastic costs. We further extend the analysis to more structured settings such as supply-oblivious arrivals and hard supply constraints, obtaining sharper guarantees that improve upon previous bounds.

Abstract: We study online allocation problems where $n$ requests over $m$ resources arrive in an adversarial order and must be served immediately and irrevocably. This framework captures both Online Resource Allocation, where the goal is to maximize value subject to resource budgets, and Online Load Balancing, where the goal is to minimize the makespan. We seek $(1\pmε)$-competitive algorithms in the large-budget or large-makespan regime. We consider a sampling model that generalizes the following two well-studied sampling models. In the Single-Sample Prophet Inequality ($\mathsf{SSPI}$) model, request $t$ is drawn from an unknown distribution $\mathcal{D}_t$, and the algorithm is given one independent sample from each $\mathcal{D}_t$ before the online phase. In the $p$-$\mathsf{Sample}$ model, the requests are adversarial, but a uniformly random $p$-fraction is revealed upfront as training data. Although near-optimal algorithms are known in the easier random-order model ($\mathsf{RO}$), where the requests arrive in a uniformly random order, prior algorithms for $\mathsf{SSPI}$ and $p$-$\mathsf{Sample}$ were problem-specific and incurred substantially worse dependencies on $ε$, $m$, and $n$. Our main contribution is a general framework that converts $\mathsf{RO}$ algorithms into algorithms for the $p$-$\mathsf{Preview}$ model, a model that generalizes both $\mathsf{SSPI}$ and $p$-$\mathsf{Sample}$. As consequences, we obtain near-optimal bounds for Online Resource Allocation, generalized Online Load Balancing, and online mixed packing-covering problems in these adversarial-order sampling models, significantly improving the bounds of [Ghuge, Singla, Wang (STOC'25)] and [Gupta and Molinaro (SODA'26)].

Abstract: The $k$-server conjecture states that a deterministic online algorithm can achieve competitive ratio $k$ on every metric space. We prove the conjecture. Specifically, we show that the work function algorithm satisfies it. Our proof uses a natural algebraic representation of the work function as a matrix, which encodes all feasible paths to reach a configuration. In this representation, the minimum and addition operations arising in the definition of optimal costs correspond to addition and multiplication of formal expressions, and each work function value corresponds to the determinant of $k$ columns of the matrix. A request arrival updates the representation via a change of basis and row replacement. The amortized analysis is based on a potential function defined in terms of a larger matrix whose coordinates are pairs of coordinates of the original matrix representation.

Abstract: Large language model agents are increasingly deployed for long-horizon task execution. However, current evaluation paradigms face three major limitations: terminal-only assessment ignores intermediate processes and struggles to localize errors efficiently and accurately, single-reference matching penalizes valid alternative solution paths, and post-hoc trajectory judging incurs high costs without the ability to halt failed runs early. To address these issues, we propose DynSTEER, a dynamic stage-wise trajectory evaluation framework for agents. DynSTEER segments rollouts into stages anchored by key completed actions, focusing evaluation on essential milestones with adequate context while enabling targeted strategy adjustments. It compiles a path-tolerant milestone graph from public task views to respect diverse legitimate strategies without leaking ground truth. Furthermore, it adaptively routes evaluation queries across multi-tier judges and halts unrecoverable executions online to curb resource waste. Experiments demonstrate that DynSTEER improves evaluation discriminability across LLM agents by 85.2\% over native evaluation, separates all model pairs with statistical significance, and saves 34.51\% of execution steps on failed rollouts.

Abstract: Accurate job runtime prediction can improve scheduling-aware resource management in grid and distributed computing environments, but prediction models must be evaluated under realistic deployment constraints. This paper revisits CPU burst time prediction on the GWA-T-4 AuverGrid workload trace and reformulates it as leakage-safe pre-execution job runtime prediction. We define the target as job-level runtime, use only submission-time attributes, exclude post-execution variables, and evaluate models under temporal and cold-start settings rather than relying only on random cross-validation. We compare standard regressors, chronological historical baselines, categorical encoding strategies, and CatBoost with native categorical handling. We further add temporal hyperparameter tuning, runtime predictability analysis, feature ablation, error analysis by job length, and a minimal scheduling simulation. After temporal-validation tuning, CatBoost achieves the strongest deployment-oriented result with R^2=0.239, MAE=27,019, RMSE=46,587, and LogMAE=2.646 on the held-out temporal test set. A single-server simulation over all 69,523 held-out temporal test jobs shows that prediction-informed SJF reduces average waiting time by 50.92% relative to FCFS. The results show that random-split evaluation overestimates performance, categorical-native boosting improves temporal generalization, and long-job underestimation remains a scheduler-relevant challenge.

Abstract: The chance-constrained correlated equilibrium concept provides a robust coordination technique for self-interested agents whose costs are uncertain to a central coordinator, but the number of joint actions considered in its computation grows exponentially with the number of agents. We propose an exact-one resource-assignment restriction for games in which agents compete for shared resources and simultaneous use of a resource is undesirable or unsafe. The restriction allows each resource to be assigned to exactly one agent, reducing the number of joint actions considered from O(2^(nr)) to O(n^r) for n agents and r resources. The resulting problem is solved over the restricted joint action set while retaining all incentive constraints associated with unilateral deviations. We show that the feasible set of the restricted problem is exactly the convex hull of the chance-constrained pure Nash equilibria contained in the exact-one assignment set, yielding a necessary and sufficient condition for nonemptiness. We further derive a sufficient condition under which all chance-constrained pure Nash equilibria of the unrestricted game are retained by the restriction. Numerical experiments in a vertiport departure-corridor coordination scenario demonstrate a 99.81% reduction in median computation time relative to the unrestricted formulation while achieving equivalent coordination performance.

Abstract: Aggregate performance in smart mobility systems depends heavily on the emergent behavior of selfish, resource-sharing agents that participate within the systems. As a result, recent work has focused on how a system designer can leverage incentives to influence behavior so that system cost (e.g., traffic congestion) is minimized. These results show that worst-case equilibria can be quite inefficient compared to system-optimal allocations. However, it is unclear to what extent agents are ``satisfied'' with their decisions in these worst-case scenarios. We demonstrate that in any incentivized atomic congestion game, agents' aggregate satisfaction at equilibrium (relative to their actions in an optimal allocation) is correlated with the efficiency of the corresponding system cost, in the sense that if agents are very satisfied with their equilibrium choices, the equilibrium must be relatively efficient. Further, we show that worst-case Nash equilibria are fragile, as every agent is indifferent between their action in a worst-case equilibrium and their action in a system-optimal allocation. In summary, at equilibrium, either agents are highly satisfied with their decisions or their decisions are highly inefficient, but both cannot be true simultaneously. This work adds to recent results for other classes of games which indicate that worst-case equilibrium efficiency guarantees only occur when agents are indifferent about their decisions.

Abstract: This paper presents significant upper-bound improvements for dynamic 2D square bin packing, where square items arrive and depart over time and the objective is to minimize the peak number of concurrent active unit bins. In our model, repacking is permitted only within a destination bin upon item arrival; migration between active bins is strictly forbidden. By introducing a streamlined two-list algorithm and proving a tight $5/16$ occupied-area bound for Next-Fit Decreasing Height, we reduce the upper bound on the asymptotic competitive ratio for arbitrary squares from 4.2154 down to 3.918, breaking a longstanding theoretical ceiling. For restricted variants, we establish asymptotic competitive ratios of at most 3.356 for unit-fraction side lengths and 2.211 for power-fraction side lengths.