Online Resource Allocation

LLM scheduling is critical to serving, yet it remains unclear how well existing designs fit agentic serving--with LLM requests issued by agents instead of humans. This shifts the workload in two ways: (1) agents act only on complete responses, making the cluster's tokens per second (TPS) the primary goal and relaxing--not eliminating--per-token latency requirements; and (2) requests share much of their KV$-reuse exceeds 80% of request tokens in a production trace from BAILIAN, versus 54-62% in chat. This paper first contributes a systematic study of request scheduling for agents on two real-world traces. We find that to increase KV$ reuse, existing schedulers overly prioritize routing requests to instances caching their KV$, overloading a few while leaving the rest idle, capping TPS. We thus present two key insights: (1) load balance need not sacrifice all KV$ reuse, thanks to the global-tier KV$ store and (2) by utilizing the workload's intra-session locality, balancing a small fraction of requests--the first request in each agent session--suffices to balance the cluster without sacrificing most KV$ reuse on local instances. SMETRIC realizes these insights with balanced session-centric scheduling: it routes each session's first request purely for load balance and its follow-up requests in a cache-aware manner, preserving load balance and local reuse while keeping demand on the global tier low. Using the session turn information as the scheduling metric is deliberate: it is derived efficiently and accurately from the user inputs alone, so the scheduler stays clean and stateless. SMETRIC improves cluster TPS by 10-16% under prefill-decode colocation with a global store and prefill TPS by 2-34% under disaggregation over state-of-the-art schedulers, also with a better per-token latency.

Online truckload bid acceptance is a closed-loop stochastic decision problem in which a carrier or broker must, in real time, accept or reject a tendered load subject to operational feasibility, fleet repositioning costs, and opportunity cost against future demand. Public, reproducible benchmarks for this problem are scarce: existing routing benchmarks are static, while dynamic-fleet studies typically rely on private operator data. We introduce FreightBidBench, a public-calibrated, dependency-free, closed-loop benchmark in which feasibility (pickup reach, appointment windows, simplified hours-of-service, stochastic yard delays) and economics (service-failure penalty, terminal fleet value, daily price-premium window) are explicit, versioned, and reproducible from public Freight Analysis Framework and U.S. Department of Agriculture truck rate data. We develop two full-horizon hindsight ceilings: a simple LP style relaxation and a tighter Lagrangian-per-truck information relaxation that retains per-truck hours-of-service and sequencing structure and is 20.7% tighter than the LP relaxation on a tight-capacity scenario and 39.3% tighter on a scarce-capacity scenario. We introduce a parametric surrogate-rollout cascade with boundary-band and scarcity-pressure escalation triggers. On ten-seed tight and scarce scenarios, the best simple policy retains 91.0% and 86.5% of rollout profit and the standard-library surrogate 94.2% and 89.3%; a cascade at a single escalation band recovers roughly 98% on both at 40-56% of rollout's mean decision latency, and on the tight scenario is statistically indistinguishable from the rollout teacher (paired-bootstrap 95% CI on the profit delta spans zero).

We study the online routing problem in large language model serving, where requests arrive sequentially and must be dispatched to parallel decode workers under tight batch-size and KV-cache constraints. Unlike widely used routing heuristics that are not tied to explicit service-level objectives (SLOs) and offer limited control over latency-throughput trade-offs, we introduce a multi-objective optimization framework that formulates routing as an online linear programming with interpretable decision rewards. We apply an efficient bid-price control policy based on the online linear programming that admits requests when their SLO-weighted benefit exceeds their shadow prices. To meet millisecond decision requirements, we develop a warm-started, projected first-order updates that track the evolving dual shadow prices online with predictable runtime. We integrate our router into the Vidur simulator and demonstrate substantial improvements over standard baselines across multiple SLO regimes, including end-to-end latency, time-to-first-token, throughput, and tail performance. A big picture from our result: a science-based approach outperforms others based on heuristics.

Real-time interaction models -- Moshi, MiniCPM-o, Qwen-Omni -- turn serving into a periodic real-time task: on every frame a session ingests streaming audio and must respond by a recurring wall-clock deadline, while its KV cache grows monotonically and stays pinned for the whole conversation. This regime hides a dangerous failure mode. On a real full-duplex stack, sustained load does not degrade serving gracefully: it falls off a cliff, jumping in one step from milliseconds per frame to a stalled engine when accumulated session state exhausts the KV pool. The collapse is metastable -- identical five-minute runs collapse or survive on run-to-run variance -- and silent: latency and deadline-miss metrics read healthy throughout. We show one move restores both stability and observability: bound each session's resident state, and latency starts telling the truth. Metronome's in-engine KV window eliminates the collapse (0/20 vs. 14/20 runs across two batches) and turns per-frame latency into a monotone load signal, on which an online admission controller discovers the schedulable concurrency; without the window, the identical controller over-admits into the wall. A first-order model predicts the collapse time within a few percent on the headline model, and a quality probe validates the bound's design by ablation: the window alone is quality-free in turn-based decoding, and its few pinned attention-sink tokens are what keep free-running generation healthy. Everything is measured end-to-end on real audio, across four interaction models on one GPU.

We study online resource allocation when both rewards and consumption sizes may be continuously distributed. Requests arrive sequentially and must be accepted or rejected irrevocably under fixed resource capacities. Each request belongs to one of finitely many observable types; conditional on an observable request type, both the reward and the scalar size are random, and the realized size scales a fixed type-specific resource-consumption vector. The model allows the deterministic fluid relaxation to be degenerate. We show that additive regret is governed by the size-weighted mass of requests whose value-to-size ratios lie near the active acceptance cutoffs. We formalize this quantity through an active weighted-mass exponent p. When p > 1, this cutoff mass is thin, and the problem is genuinely hard: every online policy must incur regret of order at least $T^{1/2 - 1/(2p)}$, and this holds for every p > 1. A sample-path marginal policy matches this lower bound up to polylogarithmic factors; and when p = 1, so that the mass grows linearly near the cutoff, it attains $O((\log T)^2)$ regret. For example, if the size and the value-to-size ratio are independent and uniformly distributed, then p = 1; if instead the size and the reward are independent and uniformly distributed, then p = 2. Thus the policy achieves $o(\sqrt{T})$ regret throughout this regularity class without any fluid non-degeneracy assumption, allowing both primal degeneracy and dual non-uniqueness.

This paper studies additive regret in the multi-secretary problem, defined as the gap between the expected offline prophet reward and the reward of the best online policy. Prior work established $O(\log T)$ regret for bounded-density distributions with connected support and $O((\log T)^2)$ upper bounds for bounded-density distributions with support gaps. It was unknown whether the extra logarithmic factor is necessary even in the one-resource model. We prove that it is necessary. For a mixture of two separated uniform distributions at the critical capacity, the optimal regret grows at least on the order of $(\log T)^2$. Thus the existing $O((\log T)^2)$ upper bounds for bounded-density gapped instances, including those implied by network revenue management models with continuous rewards, are tight in this simplest specialization. The same framework also yields a matching lower bound for gapped distributions whose gap-facing densities vanish near the support edges; this companion result is given in the appendix. The proofs use Bellman certificates: feasible solutions to a relaxation of the exact Bellman recursion. This framework converts lower bounds into explicit certificate constructions and identifies why support gaps permit larger regret.

We present a multi-agent system for studying the allocation of discrete, congested resources among heterogeneous strategic agents, motivated by the problem of railway slot allocation under deregulation. Multiple operator-agents, differing in size and capacity, interact through a shared auction mechanism over repeated rounds under time-constrained decision-making. The mechanism combines a congestion-based base price that increases with aggregate demand with an asymmetric corrective adjustment that penalises the agent requesting the most slots and rewards the agent requesting the fewest, and is designed to mitigate strategic dominance by large agents while preserving transparency and congestion sensitivity. We formulate the interaction as a repeated game with incomplete information and implement the system as a real-time, web-based multi-agent environment in which human participants control individual agents and observe live marginal-cost and competitor feedback. We report exploratory observations from two structured sessions with domain experts acting as operator-agents. The congestion mechanism responds to aggregate demand as designed and the corrective incentives are actively triggered, but agents representing large operators persist with high-request strategies despite the penalty, suggesting that corrective pricing is necessary but not sufficient to neutralise strategic dominance in this multi-agent setting. A post-session debrief indicates that participants' decisions were driven by the assumed agent role rather than personal disposition, and provides qualitative support for strategic motives, such as preserving market presence and raising rivals' costs, operating alongside short-term profit maximisation. We discuss implications for multi-agent mechanism design under asymmetric budgets and outline directions for analytical validation and larger-scale multi-agent experiments.

Robotics foundation models (RFMs) are making general-purpose robots increasingly practical for factory deployments. While RFM serving systems are central to this vision, existing systems are largely shaped by a single-robot, single-model assumption: inference is treated as an edge-computing problem handled by an on-robot or dedicated nearby GPU, and the serving objective is to minimize the latency of a single action model. In this paper, we propose ROSA, an RFM serving system for robot factories designed around three key principles. First, ROSA adopts shared GPU-pool serving, allowing a fleet of robots to access powerful server-class GPUs over the network in order to improve inference performance, battery duration, and GPU utilization. Second, ROSA provides a robotics-aware programming abstraction and system design that supports multi-model pipelines, per-task performance requirements, and failure handling. Third, ROSA uses factory-objective-driven scheduling to maximize SLO-qualified factory productivity rather than minimizing individual request latency. We implement ROSA on top of Ray Serve for distributed orchestration, with vLLM, PyTorch, and JAX as model-serving backends, and evaluate it on both real robots and synthetic large-scale workloads. The results show that ROSA improves factory productivity by up to 12.06x over conventional dedicated serving systems.

We study repeated bidding in multi-unit discriminatory (pay-as-bid) auctions for a single bidder with per-round utility equal to value minus $α$ times payment, where $α\in[0,1]$ is a cost-of-capital parameter. The bidder aims to maximize cumulative utility over $T$ rounds subject to a total budget $B$. The problem is challenging even without budgets: the action space is exponential in $M$, the maximum demand of the bidder and the valuation vector (context) varies over time. Exploiting a decomposition of utility across units, we develop polynomial-time learning algorithms based on shortest paths in a directed acyclic graph, obtaining sublinear regret under both full-information and bandit feedback. In the bandit setting, the regret is independent of the number of contexts due to complete cross-learning: observing the utility of the chosen action under the realized context reveals the utility for the same action under all counterfactual contexts. With budget constraints, when the average normalized per-round budget $ρ=\frac{B}{MT}<1$, we design a coupled primal-dual algorithm in which the DAG-based procedure uses dual-adjusted edge weights for primal updates, while online gradient descent updates the dual variable, yielding $ρ$-approximate sublinear regret. Finally, we give implementations whose per-round time and space are independent of the number of contexts, enabling scalability to large or even infinite context spaces.

Modern local and agentic workloads often need large-model capacity at low concurrency, but run on GPUs that cannot keep a frontier-scale model resident. Mixture-of-Experts (MoE) models are a natural fit because they activate only a small subset of experts per token, but their sparsity saves computation, not residency: the full expert pool still has to be stored, and any expert used by a layer must be in GPU memory when that layer runs. Static layer-level CPU offload makes such models fit, but transfers the expert layer in bulk on every forward pass, losing much of the sparsity advantage. We view low-resource MoE serving as a working-set problem on the GPU. Routed expert weights and the KV cache are two memory-demand streams competing for the same limited VRAM. We implement this view in WiSP (Working-Set Paging), a routing-aware expert pager that plugs into an unmodified serving engine and preserves byte-identical outputs. On a real 24 GiB RTX 3090, WiSP achieves up to 2.0x the decode throughput of static offload at the same memory budget when the model does not fit. A natural next step is to predict future experts and prefetch them. We find that this does not help in single-stream decode: the bottleneck is PCIe bandwidth, not prediction quality, so speculative transfers compete with demand transfers instead of hiding them. This shifts the design question from prefetching to allocation: how should one VRAM budget be divided between resident experts and the KV cache? We answer with MV-WSA (Marginal-Value Working-Set Allocation), which splits memory by marginal latency benefit per byte while enforcing a KV-admission floor. As a startup configurator, MV-WSA is the only policy we test that stays near-best on both prefill and decode; as a live controller, it resizes both pools while serving and reduces end-to-end time by up to 1.19x over a fixed offline split, without changing model outputs.

We study the problem of fair online resource allocation, motivated by applications such as refugee resettlement and airline scheduling, where agents arrive sequentially and must be assigned to facilities with limited capacities. We introduce a model that maximizes the overall welfare subject to resource constraints and a Lipschitz fairness requirement, which ensures that similar agents arriving in the same batch receive similar expected outcomes. We first analyze the offline problem, proving that the value of the optimal fair allocation is at least an $Ω(1/γ)$ fraction of the optimal unfair allocation, where $γ$ is the fairness coefficient, thereby bounding the price of fairness. For the online setting, we propose an algorithm based on dual mirror descent that enforces fairness constraints within batches while estimating optimal dual variables. We prove that this algorithm achieves sublinear regret relative to the optimal offline fluid benchmark. Finally, we validate our theoretical results using real-world data from the Refugee Economies Programme, demonstrating the algorithm's performance and examining the trade-offs between welfare maximization and fairness enforcement.

Long chain-of-thought (CoT) trajectories in large language model (LLM) reasoning cause severe inference bottlenecks due to rapid key-value (KV) cache growth. Current decoding-time compression methods mitigate this issue via token eviction, but typically assume a uniform budget distribution across all layers and heads. In contrast, existing non-uniform budget allocation methods are predominantly designed for the static prompt prefill phase, and they do not capture the stepwise context demands of autoregressive reasoning. To bridge this gap, we propose ReasonAlloc, a training-free framework that recasts decoding-time KV compression as a hierarchical budget allocation problem. ReasonAlloc operates at two complementary levels: an offline layer-wise preallocation strategy captures an architecture-driven demand pattern which we call ``\textit{Reasoning Wave}'', while an online head-wise strategy reallocates resources during decoding to information-rich heads based on real-time utility. Evaluations on mathematical reasoning benchmarks (MATH-500, AIME~2024) using DeepSeek-R1-Distill-Llama-8B, DeepSeek-R1-Distill-Qwen-14B, and AceReason-14B show that ReasonAlloc outperforms uniform-budget R-KV, SnapKV, and Pyramid-RKV (a baseline enforcing a static, monotonically decreasing layer budget), with the largest gains at small budgets (128-512 tokens). ReasonAlloc is plug-and-play with existing token-eviction policies and introduces negligible inference-time overhead.

Dynamic multi-resource allocation is a central problem in shared computing environments, where users' demands arrive sequentially and resources must be distributed fairly without knowledge of future demands. Existing methods emphasize fairness guarantees such as Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, but often overlook system utility. Moreover, these fairness criteria are mutually incompatible, preventing strict enforcement of them at the same time. We propose a neural allocation mechanism that reconciles fairness with utility through multi-objective optimization during sequential rollout. We first formalize fairness in the dynamic setting via stepwise loss functions for Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, enabling differentiable training. Leveraging non-wastefulness, we parameterized the solutions by constraining allocations to the subspace of demand while allowing elastic over-allocation when resources remain available. Empirical results demonstrate that our learned allocator achieves substantially higher utility at comparable levels of fairness, uncovering clear Pareto-frontier-like tradeoffs across metrics.

In modern online advertising platforms, Guaranteed Delivery (GD) contracts coexist and bid with Real-Time Bidding (RTB) auctions. Recent approaches either decouple GD and RTB optimization or rely on heuristic priority rules, and thus fail to effectively balance short-term revenue maximization with long-term contract delivery under complex multi-slot delivery and impression constraints. To address these challenges, we propose HMAF (Hierarchical Multi-Slot Allocation Framework), a unified framework designed to optimize impression allocation in GD--RTB advertising platforms. HMAF employs the Plan--Calibrate--Execute paradigm as its core structure, and integrates offline constraint optimization with online decision-making, balancing offline GD resource planning, dynamically calibrating GD--RTB competitiveness, and making real-time listwise rank decisions across multi-slot environments. HMAF has been implemented in multiple marketing scenarios at Meituan, one of the world's largest online food delivery platforms, leading to a 3.72% increase in GD delivery rate and a 1.59% increase in total advertisement revenue.

LLM post-training often relies on reinforcement learning methods that sample multiple rollouts per prompt, yet most existing approaches use a fixed rollout budget for every prompt, despite large differences in the training signal different prompts provide. In this paper, we study adaptive rollout allocation under a fixed global budget and formulate the problem as online resource allocation with prompt-level diminishing returns. Our method, CERO, maintains a Beta posterior over each prompt's success probability and uses the posterior expected Bernoulli variance as a Bayesian estimate of the value of additional rollouts. We use this estimate to construct a concave, saturating utility over cumulative allocations, yielding an objective in which decisions across prompts and epochs are coupled by the global budget. Since the resulting objective is temporally nonseparable, we derive a Fenchel-dual reformulation and update both prompt-level and budget-level dual variables via projected online gradient descent. Under fixed prompt utilities, we prove an $O(\sqrt{K})$ regret bound against the offline allocation benchmark. Experiments on mathematical-reasoning problems show that CERO consistently outperforms GRPO across multiple open-weight LLMs and benchmarks, demonstrating that adaptive rollout budgeting can improve sample efficiency.

The edge-cloud computing continuum demands self-management mechanisms that scale across autonomous administrative domains while honouring tenant- and operator-specified data sovereignty. We present Neural Pub/Sub, a federated-broker autonomic substrate whose self-organising behaviour emerges from market-based price signals rather than centralised control. Its MAPE-K control loop closes over per-broker health and load monitoring, marginal-cost clearing-price analysis, placement planning over a polymatroidal feasibility region, federated cross-domain dispatch, and shared peer subscription summaries with bounded-staleness price signals. The Plan step is anchored in a Walrasian convergence proposition: under gross-substitutes valuations on tree and series-parallel service-dependency DAGs, decentralised price-based allocation matches the welfare of a centralised oracle. We evaluate the substrate on a 4-VM, 4-domain, 48-worker federated edge-cloud testbed (single data centre, 50 ms emulated WAN) in a 1005-run campaign augmented by a fair-process-count sharded-oracle comparator. The federated market dominates a single-process oracle by 2-4% with 45 of 45 per-seed wins (sign-test p ~ 2.8e-14, Hodges-Lehmann median -39.6 ms); against a four-shard centralised orchestrator at equal process count the gap stays within +/-1.5% across all nine (pipeline, load) cells. Round-robin completion rate collapses 98.8% -> 22.4% -> 3.3% across arrival rates 5/10/15 pps while the market preserves completion; the advantage decomposes into three Walrasian properties (information completeness, admission control, price discovery). Federation withstands broker death and network partition (completion rate >= 98.7% across 75 cells), and sovereignty enforcement adds no measurable runtime overhead across 60 governance-grid runs. Heterogeneous-domain stressors and cross-site WAN deployment remain future work.

A properly calibrated rule-based autoscaler can beat every one of six mainstream deep reinforcement learning (DRL) algorithms on cost across every workload we test - so when, if ever, does DRL actually help? We study this in RLScale-Bench, a reproducible benchmark and evaluation protocol for DRL on adaptive resource control, where an agent allocates compute to a dynamic workload under cost and service-level constraints. We evaluate PPO, DQN, A2C, SAC, TD3, and DDPG under matched architectures, training budgets, and reward functions against a calibrated rule-based baseline across six workload patterns and five seeds (240 runs), instantiate the benchmark on Kubernetes Horizontal Pod Autoscaling, and probe distribution-shift generalization. Three findings challenge common assumptions: (i) the calibrated controller achieves the lowest cost on all six workloads, though it trails the best RL agents on bursty and flash traffic; (ii) discrete-action algorithms outperform continuous-action ones by one to two orders of magnitude in constraint violations due to action-space mismatch; and (iii) no single algorithm dominates across workloads, with rankings shifting by up to four positions. The bottleneck in RL-based resource control is not algorithm selection but baseline calibration, reward engineering, and realistic evaluation protocols.

Intelligent scaling of microservices in cloud platforms is crucial for mitigating escalating compute costs while avoiding service disruptions. Current solutions are limited to the univariate space, typically focusing on CPU usage alone to drive scaling decisions. Moreover, they address the problem as a purely forecasting task, focusing on prediction precision while neglecting the greater risks of underestimation and delays in system responsiveness. Alternative solutions are computationally complex, making them impractical for large-scale, real-time deployments. To address these challenges, we present STARIXNet, a lightweight neural network that guides resource allocation decisions in the multivariate space by capturing spatio-temporal relationships among multiple system metrics. STARIXNet models multiple quasi-dependent attributes, in particular the (S)easonal, (T)emporal, (A)uto-(R)egressive (I)ntegrated, and e(X)ogenous patterns, then implements an aggregation policy to finalize scaling decisions, prioritizing service stability, followed by cost-efficiency, over raw forecast accuracy. We empirically demonstrate the performance of STARIXNet by benchmarking against existing solutions in real-world settings. STARIXNet is deployed for critical production microservices at Walmart achieving tangible savings ranging from 10% to 50%, in addition to intangible benefits through improved service stability and customer experience.

We study how an e-commerce firm should make real-time fulfillment decisions in a two-layer distribution network when multi-item customer orders arrive sequentially and future demand is unknown. The central managerial tension is whether to use scarce front distribution center (FDC) inventory to save current fulfillment cost or preserve that inventory for future orders that may be more valuable to serve locally. We formulate an adversarial online model with multiple FDCs, one regional distribution center (RDC), multi-unit multi-item orders, and item-specific and time-varying variable costs. Our theoretical objective is to characterize when simple, interpretable, and implementable fulfillment rules can perform nearly as well as an optimal clairvoyant planner. We develop a family of Gated Priority-based Greedy policies, derive competitive-ratio guarantees under both time-varying and time-invariant cost structures, and establish matching or near-matching lower bounds for any online algorithm. Numerical experiments show that the proposed policies perform strongly relative to generalized myopic and forecast-based benchmarks. The analysis yields managerial guidance on when local inventory should be protected, when splitting orders is worth the fixed-cost burden, and how the relative magnitudes of fixed and variable costs determine the value of more sophisticated optimization.

Many real-world resource allocation systems, such as humanitarian logistics and vaccine distribution, must preposition limited supply across multiple locations before demand is realized while stockouts incur irreversible service losses. To study this, we introduce the Online Shared Supply Allocation (OSSA) problem, a stateful online model in which a central hub allocates a finite, unknown supply to multiple sites facing sequential demand under fixed-charge transportation costs and lost-sales penalties. Unlike classical make-to-stock or make-to-order inventory models, OSSA precludes backlogging and replenishment only hedges against future demand. To tackle OSSA, we propose a deterministic threshold-proportional policy GPA and prove that it achieves a $4/3$-approximation to the offline optimum up to an additive term independent of the total supply. We complement this with matching lower bounds showing that the $4/3$ ratio is tight and that the additive-error dependence is unavoidable, even for randomized algorithms that know the total supply upfront. Finally, we develop a learning-augmented extension to GPA that principally incorporates imperfect forecasts (e.g., from human experts or ML models) commonly available in practice, enabling us to exploit high-quality advice while being robust against arbitrary bad ones. Synthetic and real-world experiments show that GPA outperforms natural baselines with global supply is scarce.

Agentic systems increasingly solve complex user requests by executing orchestrated workflows, where subtasks are assigned to specialized models or tools and coordinated according to their dependencies. While recent work improves agent efficiency by optimizing the performance--cost--latency frontier, real deployments often impose concrete requirements: a workflow must be completed within a specified budget and before a specified deadline. This shifts the goal from average efficiency optimization to maximizing the probability that the entire workflow completes successfully under explicit budget and deadline constraints. We study \emph{constraint-driven online resource allocation for agentic workflows}. Given a dependency-structured workflow and estimates of success rates and generation lengths for each subtask--model pair, the executor dynamically allocates models and parallel samples across simultaneously executable subtasks while managing the remaining budget and time. We formulate this setting as a finite-horizon stochastic online allocation problem and propose \emph{Monte Carlo Portfolio Planning} (MCPP), a lightweight closed-loop planner that directly estimates constrained completion probability through simulated workflow executions and replans after observed outcomes. Experiments on CodeFlow and ProofFlow demonstrate that MCPP consistently improves constrained completion probability over strong baselines across a wide range of budget--deadline constraints.

Generative Recommender (GR) inference places embedding hot caches (EMB) and KV caches in direct competition for limited GPU HBM: allocating more memory to one improves its efficiency but degrades the other. Existing systems optimize them in isolation, overlooking that the optimal EMB-KV allocation ratio can shift by up to 0.35 across workload regimes, leaving 20-30% latency improvement unrealized. While online reallocation is required to close this gap, naive approaches introduce H2D refill traffic on the critical path, causing P99 SLO violations. To address this, we present HELM, which jointly manages HBM allocation and request routing at runtime through two key components: (1) Adaptive Memory Allocation, a three-layer PPO-based controller (frozen base policy, online residual adapter, and burst-aware recovery controller) that achieves $32\,\mathrm{μs}$ decision latency while staying within 0.024-0.029 of the offline-optimal ratio; and (2) EMB-KV-Aware Scheduling, which routes requests by jointly considering KV residency, embedding locality, and node load to avoid routing inefficiencies under heterogeneous allocations. Evaluations on three production-scale datasets over a 32-node A100 cluster show that HELM reduces P99 latency by 24-38% over the best static policy and achieves 93.5-99.6% SLO satisfaction across Steady, Trend, and Burst workloads, significantly outperforming state-of-the-art baselines without sacrificing throughput.

The usage of large language models (LLMs) has grown increasingly fragmented, with no single model dominating. Meanwhile, cloud providers offer a wide range of mid-tier and older-generation GPUs that enjoy better availability and deliver comparable performance per dollar to top-tier hardware. To efficiently harness these heterogeneous resources for serving multiple LLMs concurrently, we introduce Coral, an adaptive heterogeneity-aware multi-LLM serving system. The key idea behind Coral is to jointly optimize resource allocation and the serving strategy of each model replica across all models. To keep pace with shifting throughput demand and resource availability, Coral applies a lossless two-stage decomposition that preserves joint optimality while cutting online solve time from hours to tens of seconds. Our evaluation across 6 models and 20 GPU configurations shows that Coral reduces serving cost by up to 2.79$\times$ over the best baseline, and delivers up to 2.39$\times$ higher goodput under scarce resource availability.

Treatment allocation under budget constraints is a central challenge in digital advertising: advertisers must decide which users to show ads to while spending a limited budget wisely. The standard approach follows a two-stage offline pipeline - first collect historical data to estimate heterogeneous treatment effects (HTE), then solve a constrained optimization to allocate the budget. This works well with abundant data, but fails in cold-start settings such as new campaigns, new markets, or new customer segments where little historical data exists. We propose Budget-Constrained Causal Bandits (BCCB), an online framework that learns which users respond to ads while simultaneously spending the budget, making treatment decisions one user at a time. BCCB unifies three components into a single sequential process: learning individual-level ad effectiveness, exploring users whose response is uncertain, and pacing the budget over time. We evaluated on the Criteo Uplift dataset, a large-scale advertising dataset from a real randomized controlled trial. Our key finding is a data-efficiency crossover: offline methods require approximately 10,000 historical observations to produce reliable results, while BCCB operates effectively from the very first user. Furthermore, BCCB exhibits 3-5x lower performance variance between runs, making it more practical for real campaign planning. Among purely online methods, BCCB consistently outperforms standard Thompson Sampling, budgeted Thompson Sampling, and greedy HTE estimation across all budget levels tested.

In many areas of medicine, security, and life sciences, we want to allocate limited resources to different sources in order to detect extreme values. In this paper, we study an efficient way to allocate these resources sequentially under limited feedback. While sequential design of experiments is well studied in bandit theory, the most commonly optimized property is the regret with respect to the maximum mean reward. However, in other problems such as network intrusion detection, we are interested in detecting the most extreme value output by the sources. Therefore, in our work we study extreme regret which measures the efficiency of an algorithm compared to the oracle policy selecting the source with the heaviest tail. We propose the ExtremeHunter algorithm, provide its analysis, and evaluate it empirically on synthetic and real-world experiments.

Motivated by the problem of assigning mediators to cases in the Kenyan judicial system, we study an online resource allocation problem where incoming tasks (cases) must be immediately assigned to available, capacity-constrained resources (mediators). The resources differ in their quality, which may need to be learned. In addition, resources can only be assigned to a subset of tasks that overlaps to varying degrees with the subset of tasks other resources can be assigned to. The objective is to maximize task completion while satisfying soft capacity constraints across all the resources. The scale of the real-world problem poses substantial challenges, since there are over 2000 mediators, and a multitude of combinations of geographic locations (87) and case types (12) that each mediator is qualified to work on. Together, these features-unknown quality of new resources (newly onboarded mediators), soft capacity constraints (due to the mandate to assign cases without delay), and high-dimensional state space-make existing scheduling and resource allocation algorithms either inapplicable or inefficient. We formalize the problem in a tractable manner, using a quadratic program formulation for assignment and a multi-agent bandit style framework for learning. We demonstrate the key properties and advantages of our new algorithm, SMaRT (Selecting Mediators that are Right for the Task), compared with baselines on some stylized instances of the mediator allocation problem. We then turn to considering its application to real-world data on cases and mediators from the Kenyan Judiciary. SMaRT outperforms baselines and allows for controlling the tradeoff between the strictness of the capacity constraints and overall case resolution rates, both in situations where mediator quality is known beforehand and when the problem is bandit-like in that learning is part of the problem definition.

We study online fair allocation of $T$ sequentially arriving items among $n$ agents with heterogeneous preferences, with the objective of maximizing generalized-mean welfare, defined as the $p$-mean of agents' time-averaged utilities, with $p\in (-\infty, 1)$. We first consider the i.i.d. arrival model and show that the pure greedy algorithm -- which myopically chooses the welfare-maximizing integral allocation -- achieves $\widetilde{O}(1/T)$ average regret. Importantly, in contrast to prior work, our algorithm does not require distributional knowledge and achieves the optimal regret rate using only the online samples. We then go beyond i.i.d. arrivals and investigate a nonstationary model with time-varying independent distributions. In the absence of additional data about the distributions, it is known that every online algorithm must suffer $Ω(1)$ average regret. We show that only a single historical sample from each distribution is sufficient to recover the optimal $\widetilde{O}(1/T)$ average regret rate, even in the face of arbitrary non-stationarity. Our algorithms are based on the re-solving paradigm: they assume that the remaining items will be the ones seen historically in those periods and solve the resulting welfare-maximization problem to determine the decision in every period. Finally, we also account for distribution shifts that may distort the fidelity of historical samples and show that the performance of our re-solving algorithms is robust to such shifts.

We study history-dependent online problems with a possibly inaccurate prediction of the future request sequence. Motivated by several real-world applications, we introduce a \emph{bounded-influence} framework in which past decisions and requests affect the future optimal value by only a bounded amount. Within this framework, we develop AdaSwitch, a meta-algorithm that adaptively switches between suitable offline and online oracles. AdaSwitch provides explicit guarantees on expected performance that tighten as prediction error decreases or the offline optimum increases. With perfect predictions, its guarantee approaches the offline oracle's guarantee as the offline optimum grows. It also retains a worst-case guarantee close to that of the online oracle under arbitrary predictions. Applications to online lead-time quotation, $k$-server and caching, and online reusable resource allocation demonstrate the framework's applicability to both reward maximization and cost minimization.

Deep learning training commonly runs on shared multi-tenant GPU servers, where exclusive allocation provides isolation but can leave resources underutilized and increase queueing time. Collocation can improve efficiency, but interference-agnostic placement may cause severe slowdowns, while inaccurate memory information can lead to out-of-memory (OOM) failures. We present AEGIS, a server-scale runtime scheduling system for controlled collocation of deep learning training workloads on shared multi-GPU servers. AEGIS integrates memory feasibility, post-placement observation, runtime-pressure filtering, placement, and OOM-aware recovery in a single scheduling loop. After placement, AEGIS observes workload activity before permitting further collocation, then uses low-overhead telemetry to determine whether a GPU can safely accept additional work. OOM failures trigger retries under progressively safer memory conditions, eventually falling back to exclusive execution. This online approach avoids costly offline pairwise compatibility profiling. We evaluate AEGIS using vision, Transformer, recommendation, and LLM-style workloads across three production-derived traces. AEGIS reduces geometric-mean makespan by 16% relative to Lucid, 21% relative to Horus, and 27% relative to exclusive allocation. Sensitivity studies show that activity-anchored observation and runtime-pressure filtering balance conservative isolation against interference-agnostic collocation, improving makespan while limiting sharing-induced per-task slowdown.

We study the dynamic allocation of indivisible resources to strategic agents under long-term constraints, where the planner aims to maximize social welfare, satisfy multiple constraints, and elicit near-truthful reports. We find standard primal-dual methods fragile in this setting: agents easily manipulate their reports to distort dual variables, sacrificing social efficiency for individual utility. To address this, we propose the Incentive-Aware Primal-Dual (IAPD) framework. On the primal side, we integrate three components to suppress manipulation: a VCG-based payment neutralizes immediate misreporting benefits, while epoch-based lazy updates and random exploration together ensure potential future gains are outweighed by immediate penalties. On the dual side, to overcome a learning barrier due to lazy updates -- which we call the "price of incentives" -- we design a novel optimistic online learning algorithm, O-FTRL-FP. It utilizes a fixed-point oracle to resolve the circular dependency between optimistic dual variables and the resulting allocations. Ultimately, our mechanism attains $\tilde{\mathcal O}(\sqrt T)$ social welfare regret, satisfies all long-term constraints, and induces a near-truthful equilibrium. It also smoothly generalizes to multi-unit multi-demand allocation problems. Notably, this $\tilde{\mathcal O}(\sqrt T)$ regret near-matches the non-strategic $Ω(\sqrt T)$ lower bound, demonstrating that incentive-awareness can be accommodated at nearly no cost.