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Yiding Feng

Publications and source records attributed to Yiding Feng.

At least 19 recordsLinked to original sources
arXiv2026

Dynamic Pricing and Advertising with Demand Learning

We consider a novel pricing and advertising framework in which a seller not only sets the product price but also designs flexible advertising schemes to influence customers' valuations of the product. We impose no structural restriction on the seller's feasible advertising strategies and allow her to advertise the product by disclosing or concealing any information. Following the information design literature, we model this fully flexible advertising as the seller choosing an arbitrary information policy that signals the product quality to customers. Customers observe the advertising signal and form a Bayesian posterior belief over the product quality. We investigate two questions in this work: (1) What is the value of advertising? To what extent can advertising enhance a seller's revenue? (2) Without any a priori knowledge of the customers' demand function, how can a seller adaptively learn and optimize both pricing and advertising strategies using past purchase responses? To study the first question, we quantify the value of advertising by comparing the optimal revenue from jointly designing advertising and a single posted price with the optimal revenue from pricing alone. We show that advertising can increase revenue by at most a factor of two, and this bound is tight. For the second question, we study the seller's dynamic pricing and advertising problem under demand uncertainty. Our main result for this question is a computationally efficient online algorithm that achieves the optimal $O(T^{2/3} (m\log T)^{1/3})$ regret rate when the valuation function is linear in the product quality. Here, $m$ is the cardinality of the discrete product quality domain and $T$ is the time horizon.

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arXiv2026

General Non-Clairvoyant KV-Cache Scheduling via Regime-Aware Routing

We study non-clairvoyant scheduling for batched Large Language Model (LLM) inference under a hard Key-Value (KV) cache memory budget. Each request has a known prompt length but an unknown response length, and its memory footprint comprises a fixed prompt component together with a response component that grows with each decoded token. At each decoding round, the scheduler chooses a feasible batch of active requests; evicting a request discards its accumulated cache states, wasting prior computation. The goal is to minimize total completion time against the optimal clairvoyant schedule that knows all response lengths. We present the first constant-competitive algorithm for arbitrary prompt lengths and arbitrary response lengths with no additional assumptions. Rather than relying on a single universal scheduling policy, our algorithm is built on a novel regime-aware routing framework. Specialized sub-schedulers handle different memory-growth geometries, while a meta-scheduler time-shares the memory budget across them and dynamically routes each job as its execution progressively reveals its behavior. This framework also yields constant-competitive guarantees for makespan and for total completion time under online arrivals.

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arXiv2026

No-Regret Bayesian Recommendation to Homogeneous Users

We introduce and study the online Bayesian recommendation problem for a recommender system platform. The platform has the privilege to privately observe a utility-relevant \emph{state} of a product at each round and uses this information to make online recommendations to a stream of myopic users. This paradigm is common in a wide range of scenarios in the current Internet economy. The platform commits to an online recommendation policy that utilizes her information advantage on the product state to persuade self-interested users to follow the recommendation. Since the platform does not know users' preferences or beliefs in advance, we study the platform's online learning problem of designing an adaptive recommendation policy to persuade users while gradually learning users' preferences and beliefs en route. Specifically, we aim to design online learning policies with no \emph{Stackelberg regret} for the platform, i.e., against the optimal benchmark policy in hindsight under the assumption that users will correspondingly adapt their responses to the benchmark policy. Our first result is an online policy that achieves double logarithmic regret dependence on the number of rounds. We also present an information-theoretic lower bound showing that no adaptive online policy can achieve regret with better dependency on the number of rounds. Finally, by formulating the platform's problem as optimizing a linear program with membership oracle access, we present our second online recommendation policy that achieves regret with polynomial dependence on the number of states but logarithmic dependence on the number of rounds.

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arXiv2026

Non-Stationary Online Resource Allocation: Learning from a Single Sample

We study online resource allocation under non-stationary demand with a minimum offline data requirement. In this problem, a decision-maker must allocate multiple types of resources to sequentially arriving queries over a finite horizon. Each query belongs to a finite set of types with fixed resource consumption and a stochastic reward drawn from an unknown, type-specific distribution. Critically, the environment exhibits arbitrary non-stationarity -- arrival distributions may shift unpredictably-while the algorithm requires only one historical sample per period to operate effectively. We distinguish two settings based on sample informativeness: (i) reward-observed samples containing both query type and reward realization, and (ii) the more challenging type-only samples revealing only query type information. We propose a novel type-dependent quantile-based meta-policy that decouples the problem into modular components: reward distribution estimation, optimization of target service probabilities via fluid relaxation, and real-time decisions through dynamic acceptance thresholds. For reward-observed samples, our static threshold policy achieves $\tilde{O}(\sqrt{T})$ regret. For type-only samples, we first establish that sublinear regret is impossible without additional structure; under a mild minimum-arrival-probability assumption, we design both a partially adaptive policy attaining the same $\tilde{O}({T})$ bound and, more significantly, a fully adaptive resolving policy with careful rounding that achieves the first poly-logarithmic regret guarantee of $O((\log T)^3)$ for non-stationary multi-resource allocation. Our framework advances prior work by operating with minimal offline data (one sample per period), handling arbitrary non-stationarity without variation-budget assumptions, and supporting multiple resource constraints.

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arXiv2026

Searching for Optimal Prices in Two-Sided Markets

We investigate online pricing in two-sided markets where a platform repeatedly posts prices based on binary accept/reject feedback to maximize gains-from-trade (GFT) or profit. We characterize the regret achievable across three mechanism classes: Single-Price, Two-Price, and Segmented-Price. For profit maximization, we design an algorithm using Two-Price Mechanisms that achieves $O(n^2 \log\log T)$ regret, where $n$ is the number of traders. For GFT maximization, the optimal regret depends critically on both market size and mechanism expressiveness. Constant regret is achievable in bilateral trade, but this guarantee breaks down as the market grows: even in a one-seller, two-buyer market, any algorithm using Single-Price Mechanisms suffers regret at least $Ω\!\big(\frac{\log\log T}{\log\log\log\log T}\big)$, and we provide a nearly matching $O(\log\log T)$ upper bound for general one-to-many markets. In full many-to-many markets, we prove that Two-Price Mechanisms inevitably incur linear regret $Ω(T)$ due to a \emph{mismatch phenomenon}, wherein inefficient pairings prevent near-optimal trade. To overcome this barrier, we introduce \emph{Segmented-Price Mechanisms}, which partition traders into groups and assign distinct prices per group. Using this richer mechanism, we design an algorithm achieving $O(n^2 \log\log T + n^3)$ regret for GFT maximization. Finally, we extend our results to the contextual setting, where traders' costs and values depend linearly on observed $d$-dimensional features that vary across rounds, obtaining regret bounds of $O(n^2 d \log\log T + n^2 d \log d)$ for profit and $O(n^2 d^2 \log T)$ for GFT. Our work delineates sharp boundaries between learnable and unlearnable regimes in two-sided dynamic pricing and demonstrates how modest increases in pricing expressiveness can circumvent fundamental hardness barriers.

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arXiv2026

Strengthening Bulow-Klemperer-Style Results for Multi-Unit Auctions

The classic result of Bulow and Klemperer (1996) shows that in multi-unit auctions with $m$ units and $n\geq m$ buyers whose values are sampled i.i.d. from a regular distribution, the revenue of the VCG auction with $m$ additional buyers is at least as large as the optimal revenue. Unfortunately, for regular distributions, adding $m$ additional buyers is sometimes indeed necessary, so the "competition complexity" of the VCG auction is $m$. We seek proving better competition complexity results in two dimensions. First, under stronger distributional assumptions, the competition complexity of VCG auction drops dramatically. In balanced markets (where $m=n$) with MHR distributions, it is sufficient to only add $(e^{1/e} - 1 + o(1))n \approx 0.4447n$ additional buyers to match the optimal revenue -- less than half the number that is necessary under regularity -- and this bound is asymptotically tight. We provide both exact finite-market results for small value of $n$, and closed-form asymptotic formulas for general market with any $m\leq n$, and any target fraction of the optimal revenue. Second, we analyze a supply-limiting variant of VCG auction that caps the number of units sold in a prior-independent way. Whenever the goal is to achieve almost the optimal revenue, this mechanism strictly improves upon standard VCG auction, requiring significantly fewer additional buyers. Together, our results show that both stronger distributional assumptions, as well as a simple prior-independent refinement to the VCG auction, can each substantially reduce the number of additional buyers that is sufficient to achieve (near-)optimal revenue. Our analysis hinges on a unified worst-case reduction to truncated generalized Pareto distributions, enabling both numerical computation and analytical tractability.

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arXiv2026

Pareto-Efficient Multi-Buyer Mechanisms: Characterization, Fairness and Welfare

A truthful mechanism for a Bayesian single-item auction results with some ex-ante revenue for the seller, and some ex-ante total surplus for the buyers. We study the Pareto frontier of the set of seller-buyers ex-ante utilities, generated by all truthful mechanisms when buyers values are sampled independently and identically (i.i.d.). We first provide a complete structural characterization of the Pareto frontier under natural distributional assumptions. For example, when valuations are drawn i.i.d. from a distribution that is both regular and anti-MHR, every Pareto-optimal mechanism is a second-price auction with a reserve no larger than the monopoly reserve. Building on this, we interpret the problem of picking a mechanism as a two-sided bargaining game, and analyze two canonical Pareto-optimal solutions from cooperative bargaining theory: the Kalai-Smorodinsky (KS) solution, and the Nash solution. We prove that when values are drawn i.i.d. from a distribution that is both regular and anti-MHR, in large markets both solutions yield near-optimal welfare. In contrast, under worst-case MHR distributions, their performance diverges sharply: the KS solution guarantees one-half of the optimal welfare, while the Nash solution might only achieve an arbitrarily small fraction of it. These results highlight the sensitivity of fairness-efficiency tradeoffs to distributional structure, and affirm the KS solution as the more robust notion of fairness for asymmetric two-sided markets.

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arXiv2026

Is This Predictor More Informative than Another? A Decision-Theoretical Comparison

In many real-world applications, a model provider provides probabilistic forecasts to downstream decision-makers who use them to make decisions under diverse payoff objectives. The provider may have access to multiple predictive models, each potentially miscalibrated, and must choose which model to deploy in order to maximize the usefulness of predictions for downstream decisions. A central challenge arises: how can the provider meaningfully compare two predictors when neither is guaranteed to be well-calibrated, and when the relevant decision tasks may differ across users and contexts? To answer this, our first contribution introduces the notion of the informativeness gap between any two predictors, defined as the maximum normalized payoff advantage one predictor offers over the other across all decision-making tasks. Our framework strictly generalizes several existing notions: it subsumes U-Calibration and Calibration Decision Loss, which compare a miscalibrated predictor to its calibrated counterpart, and it recovers Blackwell informativeness as a special case when both predictors are perfectly calibrated. Our second contribution is a dual characterization of the informativeness gap, which gives rise to a natural informativeness measure that can be viewed as a relaxed variant of the earth mover's distance between two prediction distributions. We show that this measure satisfies natural desiderata: it is complete and sound, and it can be estimated sample-efficiently in the prediction-only access setting. We complement our theory with experiments on LLM-based forecasters in real-world prediction tasks, showing that the informativeness gap offers a more decision-relevant alternative to traditional metrics, and provides a principled lens for evaluating how ad hoc calibration post-processing affects downstream decision usefulness.

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arXiv2026

Contracting with a Mechanism Designer

This paper explores the economic interactions within modern crowdsourcing markets. In these markets, employers issue requests for tasks, platforms facilitate the recruitment of crowd workers, and workers complete tasks for monetary rewards. Recognizing that these roles serve distinct functions within the ecosystem, we introduce a three-party model that distinguishes among the principal (the requester), the intermediary (the platform), and the pool of agents (the workers). The principal, unable to directly engage with agents, relies on the intermediary to recruit and incentivize them. This interaction unfolds in two stages: first, the principal designs a profit-sharing contract with the intermediary; second, the intermediary implements a mechanism to select an agent to complete the delegated task. We analyze the proposed model as an extensive-form Stackelberg game. Our contributions are threefold. First, we fully characterize the subgame perfect equilibrium of our model. In particular, the principal's contract design problem can be represented as virtual value pricing, a novel auction-theoretic formulation. We identify the optimality of linear contracts, even when the task has multiple outcomes and agents' cost distributions are asymmetric. Second, to quantify the principal's utility loss from delegation and information asymmetry, we introduce the price of double marginalization (PoDM) and the classical price of anarchy (PoA). We derive tight or nearly tight bounds on both ratios under regular and monotone hazard rate distributions. Finally, we extend our analysis to two natural variants of the base model: (i) the intermediary is restricted to anonymous pricing mechanisms, and (ii) the principal lacks precise information about the market size.

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arXiv2026

Simple and Robust Quality Disclosure: The Power of Quantile Partition

Quality information on online platforms is often conveyed through simple, percentile-based badges and tiers that remain stable across different market environments. Motivated by this empirical evidence, we study robust quality disclosure in a market where a platform commits to a public disclosure policy mapping the seller's product quality into a signal, and the seller subsequently sets a downstream monopoly price. Buyers have heterogeneous private types and valuations that are linear in quality. We evaluate a disclosure policy via a minimax competitive ratio: its worst-case revenue relative to the Bayesian-optimal disclosure-and-pricing benchmark, uniformly over all prior quality distributions, type distributions, and admissible valuations. Our main results provide a sharp theoretical justification for quantile-partition disclosure. For K-quantile partition policies, we fully characterize the robust optimum: the optimal worst-case ratio is pinned down by a one-dimensional fixed-point equation and the optimal thresholds follow a backward recursion. We also give an explicit formula for the robust ratio of any quantile partition as a simple "max-over-bins" expression, which explains why the robust-optimal partition allocates finer resolution to upper quantiles and yields tight guarantees such as 1 + 1/K for uniform percentile buckets. In contrast, we show a robustness limit for finite-signal monotone (quality-threshold) partitions, which cannot beat a factor-2 approximation. Technically, our analysis reduces the robust quality disclosure to a robust disclosure design program by establishing a tight functional characterization of all feasible indirect revenue functions.

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arXiv2026

Competitive Non-Clairvoyant KV-Cache Scheduling for LLM Inference

Large Language Model (LLM) inference presents a unique scheduling challenge due to the Key-Value (KV) cache, where a job's memory footprint grows linearly with the number of decoded tokens. This growth couples scheduling decisions with feasibility: a scheduler must minimize latency under a hard memory budget, yet the response lengths of requests are inherently unknown. While recent works have explored this problem either assuming clairvoyance -- exact knowledge of response lengths -- or relying on machine-learned predictions, obtaining robust performance guarantees without any prior knowledge of job sizes remains a theoretically fundamental and practically important open problem. In this work, we propose the Geometric Slicing Algorithm (GSA), the non-clairvoyant policy to achieve the first constant competitive ratio for this problem in the offline batch setting. GSA manages uncertainty through a geometric phase structure that periodically restarts jobs to bound memory exposure, combined with a staggered pipeline mechanism that enables high concurrency by smoothing aggregate memory consumption. We prove that GSA achieves a competitive ratio of at most 61.92 for general instances, improving to 32 in the large-memory regime. Our algorithmic framework also yields a clairvoyant counterpart, the Geometric Batching Algorithm (GBA), which achieves an approximation ratio of 10.67 for general instances and 6.75 in the large-memory regime -- significantly improving upon the best previously known bound of over 9000. Numerical experiments on real request traces demonstrate that our algorithms perform robustly while preserving these worst-case guarantees.

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arXiv2025

Near-Optimal Bayesian Online Assortment of Reusable Resources

Motivated by the applications of rental services in e-commerce, we consider revenue maximization in online assortment of reusable resources for a stream of arriving consumers with different types. We design competitive online algorithms with respect to the optimum online policy in the Bayesian setting, in which types are drawn independently from known heterogeneous distributions over time. In the regime where the minimum of initial inventories $c_0$ is large, our main result is a near-optimal $1-\min\left(\frac{1}{2},\sqrt{\log(c_0)/c_0}\right)$ competitive algorithm for the general case of reusable resources. Our algorithm relies on an expected LP benchmark for the problem, solves this LP, and simulates the solution through an independent randomized rounding. The main challenge is obtaining point-wise inventory feasibility in a computationally efficient fashion from these simulation-based algorithms. To this end, we use several technical ingredients to design $\textit{discarding policies}$ -- one for each resource. These policies handle the trade-off between the inventory feasibility under reusability and the revenue loss of each of the resources. However, discarding a unit of a resource changes the future consumption of other resources. To handle this new challenge, we also introduce $\textit{post-processing}$ assortment procedures that help with designing and analyzing our discarding policies as they run in parallel, which might be of independent interest. As a side result, by leveraging techniques from the literature on prophet inequality, we further show an improved near-optimal $1-1/\sqrt{c_0+3}$ competitive algorithm for the special case of non-reusable resources. We finally evaluate the performance of our algorithms using the numerical simulations on the synthetic data.

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arXiv2025

Robustness of Online Inventory Balancing to Inventory Shocks

In classic adversarial online resource allocation problems such as AdWords, customers arrive online while products are given offline with a fixed initial inventory. To ensure revenue guarantees under uncertainty, the decision maker must balance consumption across products. Based on this, the prevalent policy "inventory balancing (IB)" has proved to be optimal or near-optimal competitive in almost all classic settings. However, these models do not capture various forms of inventory shocks on the supply side, which play an important role in real-world online assortment and can significantly impact the revenue performance of the IB algorithm. Motivated by this paradigm, we introduce a variant of online assortment planning with inventory shocks. Our model considers adversarial exogenous shocks (where supply increases unpredictably) and allocation-coupled endogenous shocks (where an inventory reduction is triggered by the algorithms and re-adjusted after a usage duration), whose combination leads to non-monotonic inventory fluctuations. As our main result, we show the robustness of IB-type strategies against such shocks by designing a new family of optimal competitive algorithms called "Batched Inventory Balancing (BIB)." Using a novel randomized primal-dual method, we bound the competitive ratio of BIB against optimal offline. We show that with proper choice of a certain parameter, this competitive ratio is asymptotically optimal and converges to (1-1/e) as initial inventories grow, in contrast to the original IB which no longer achieves the optimal ratio in this new model. Moreover, we characterize BIB's competitive ratio parametric by its penalty function and show that it matches exactly the competitive ratio of IB without shocks. Our refined analysis reduces the dual construction to a combinatorial "interval assignment problem" whose algorithmic solution may be of independent interest.

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arXiv2025

Contextual Search in Principal-Agent Games: The Curse of Degeneracy

In this work, we introduce and study contextual search in general principal-agent games, where a principal repeatedly interacts with agents by offering contracts based on contextual information and historical feedback, without knowing the agents' true costs or rewards. Our model generalizes classical contextual pricing by accommodating richer agent action spaces. Over $T$ rounds with $d$-dimensional contexts, we establish an asymptotically tight exponential $T^{1 - Θ(1/d)}$ bound in terms of the pessimistic Stackelberg regret, benchmarked against the best utility for the principal that is consistent with the observed feedback. We also establish a lower bound of $Ω(T^{\frac{1}{2}-\frac{1}{2d}})$ on the classic Stackelberg regret for principal-agent games, demonstrating a surprising double-exponential hardness separation from the contextual pricing problem (a.k.a, the principal-agent game with two actions), which is known to admit a near-optimal $O(d\log\log T)$ regret bound [Kleinberg and Leighton, 2003, Leme and Schneider, 2018, Liu et al., 2021]. In particular, this double-exponential hardness separation occurs even in the special case with three actions and two-dimensional context. We identify that this significant increase in learning difficulty arises from a structural phenomenon that we call contextual action degeneracy, where adversarially chosen contexts can make some actions strictly dominated (and hence unincentivizable), blocking the principal's ability to explore or learn about them, and fundamentally limiting learning progress.

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arXiv2025

Robust Dynamic Staffing with Predictions

We consider a natural dynamic staffing problem in which a decision-maker sequentially hires workers over a finite horizon to meet an unknown demand revealed at the end. Predictions about demand arrive over time and become increasingly accurate, while worker availability decreases. This creates a fundamental trade-off between hiring early to avoid understaffing (when workers are more available but forecasts are less reliable) and hiring late to avoid overstaffing (when forecasts are more accurate but availability is lower). This problem is motivated by last-mile delivery operations, where companies such as Amazon rely on gig-economy workers whose availability declines closer to the operating day. To address practical limitations of Bayesian models (in particular, to remain agnostic to the underlying forecasting method), we study this problem under adversarial predictions. In this model, sequential predictions are adversarially chosen uncertainty intervals that (approximately) contain the true demand. The objective is to minimize worst-case staffing imbalance cost. Our main result is a simple and computationally efficient online algorithm that is minimax optimal. We first characterize the minimax cost against a restricted adversary via a polynomial-size linear program, then show how to emulate this solution in the general case. While our base model focuses on a single demand, we extend the framework to multiple demands (with egalitarian/utilitarian objectives), to settings with costly reversals of hiring decisions, and to inconsistent prediction intervals. We also introduce a practical "re-solving" variant of our algorithm, which we prove is also minimax optimal. Finally we conduct numerical experiments showing that our algorithms outperform Bayesian heuristics in both cost and speed, and are competitive with (approximate or exact) Bayesian-optimal policies when those can be computed.

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arXiv2025

Online Resource Allocation with Cancellations

We initiate the study of two-sided online resource allocation with costly cancellations. Our focus is on edge-weighted online bipartite matching (and several of its extensions), where nodes arrive online and request offline resources. In contrast to the classic literature, any fraction of an offline resource that was preallocated to an earlier online node can be reclaimed, resulting in the loss of the previously allocated edge-weight plus an additional penalty equal to a non-negative constant factor $f$ times the edge-weight. Parameterizing the problem by the buyback factor $f$, our main result is the development of optimal competitive algorithms for \emph{all possible values} of $f$ through a novel primal-dual family of algorithms in the fractional (or equivalently, large capacity) setting, and establishing their optimality by deriving matching lower bounds. Interestingly, our results reveal a phase transition: for the small buyback regime ($f < \frac{e-2}{2}$), the optimal competitive ratio is $\frac{e}{e-(1+f)}$, and for the large buyback regime ($f \geq \frac{e-2}{2}$), the competitive ratio is $-W_{-1}\left(\frac{-1}{e(1+f)}\right)$, where $W_{-1}$ is the non-principal branch of the Lambert $W$ function. We also study variants of this model, such as matching with deterministic integral allocations. We again show a phase transition: for the small buyback regime ($f < \frac{1}{3}$), the optimal competitive ratio is $\frac{2}{1-f}$, while for the large buyback regime ($f \geq \frac{1}{3}$), the competitive ratio is $1 + 2f + 2\sqrt{f(1+f)}$. We further consider various extensions, including to configuration allocations and submodular welfare maximization, as well as negative values of $f$, modeling a secondary supply channels or overflow capacities available at discounted rates. Our unifying primal-dual framework achieves the exact optimal competitive ratio across all these variants

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arXiv2025

Competition Complexity in Multi-Item Auctions: Beyond VCG and Regularity

We quantify the value of the monopoly's bargaining power in terms of competition complexity--that is, the number of additional bidders the monopoly must attract in simple auctions to match the expected revenue of the optimal mechanisms (c.f., Bulow and Klemperer, 1996, Eden et al., 2017)--within the setting of multi-item auctions. We show that for simple auctions that sell items separately, the competition complexity is $Θ(\frac{n}α)$ in an environment with $n$ original bidders under the slightly stronger assumption of $α$-strong regularity, in contrast to the standard regularity assumption in the literature, which requires $Ω(n \cdot \ln \frac{m}{n})$ additional bidders (Feldman et al., 2018). This significantly reduces the value of learning the distribution to design the optimal mechanisms, especially in large markets with many items for sale. For simple auctions that sell items as a grand bundle, we establish a constant competition complexity bound in a single-bidder environment when the number of items is small or when the value distribution has a monotone hazard rate. Some of our competition complexity results also hold when we compete against the first best benchmark (i.e., optimal social welfare).

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arXiv2025

Online Job Assignment

Motivated primarily by applications in cloud computing, we study a simple, yet powerful, online allocation problem in which jobs of varying durations arrive over continuous time and must be assigned immediately and irrevocably to one of the available offline servers. Each server has a fixed initial capacity, with assigned jobs occupying one unit for their duration and releasing it upon completion. The algorithm earns a reward for each assignment upon completion. We consider a general heterogeneous setting where both the reward and duration of a job depend on the job-server pair. The objective of the online algorithm is to maximize the total collected reward, and remain competitive against an omniscient benchmark that knows all job arrivals in advance. Our main contribution is the design of a new online algorithm, termed Forward-Looking BALANCE (FLB), and using primal-dual framework to establish that it is (asymptotically) optimal-competitive. This meta-algorithm has two main primitives: (i) keeping track of the capacity used for each server at each time and applying a penalty function to this quantity, and (ii) adjusting the reward of assigning a job to a server by subtracting the total penalty of a particularly chosen subset of future times, in contrast to just looking at the current time. The FLB algorithm then assigns the arriving job to the server with the maximum adjusted reward. If R and D are the ratios of maximum over minimum rewards and durations, we show that the FLB algorithm obtains an asymptotic competitive ratio of ln(RD)+3lnln(max(R,D))+O(1). We further show this bound has optimal dependencies on all the parameters. Our main analysis combines a novel dual-fitting technique, which leverages the configuration LP benchmark for this problem, and a novel inductive argument to establish the capacity feasibility of the algorithm, which might be of independent interest.

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