arXiv subjects

Sean R. Sinclair

Publications and source records attributed to Sean R. Sinclair.

At least 19 recordsLinked to original sources

arXiv2026

Sequential Fair Allocation and Routing in Nonprofit Operations

We study a dynamic fair sequential allocation problem in which a central planner distributes a divisible resource across multiple locations under demand uncertainty. Motivated by applications such as humanitarian relief and food distribution, we incorporate routing decisions into the planner's problem and jointly optimize allocation and visitation order under two max-min fairness objectives, ex-post and forward. We first reveal an equating property of the optimal allocation for any fixed visitation order. This property is crucial to establish that the optimal allocation follows a threshold structure: at each location, demand is fully satisfied when sufficiently low and otherwise met proportionally. We then characterize the optimal routing policy and show that, under certain conditions, visiting locations in decreasing order of coefficient of variation (CV) of demand is optimal. Building on this insight, we propose a simple heuristic, PPA-deCV, which closely approximates the fairness-efficiency frontier of the jointly optimal policy. Next, through extensive numerical experiments, we compare multiple fairness objectives across different fairness metrics, demonstrating that improvements in surrogate max-min objectives do not necessarily translate into improvements in fairness metrics. Furthermore, we identify which objective is aligned with which fairness metric, providing practical guidance on objective selection to achieve fairness-efficiency trade-offs.

math.OC↗

arXiv2026

Offline-Online Reinforcement Learning for Linear Mixture MDPs

We study offline-online reinforcement learning in linear mixture Markov decision processes (MDPs) under environment shift. In the offline phase, data are collected by an unknown behavior policy and may come from a mismatched environment, while in the online phase the learner interacts with the target environment. We propose an algorithm that adaptively leverages offline data. When the offline data are informative, either due to sufficient coverage or small environment shift, the algorithm provably improves over purely online learning. When the offline data are uninformative, it safely ignores them and matches the online-only performance. We establish regret upper bounds that explicitly characterize when offline data are beneficial, together with nearly matching lower bounds. Numerical experiments further corroborate our theoretical findings.

cs.LG↗

arXiv2026

Non-Stationary Inventory Control with Lead Times

We study non-stationary single-item, periodic-review inventory control problems in which the demand distribution is unknown and may change over time. We analyze how demand non-stationarity affects learning performance across inventory models, including systems with demand backlogging or lost-sales, both with and without lead times. For each setting, we propose an adaptive online algorithm that optimizes over the class of base-stock policies and establish performance guarantees in terms of dynamic regret relative to the optimal base-stock policy at each time step. The algorithms leverage the convexity and one-sided feedback structure of inventory costs to enable counterfactual policy evaluation despite demand censoring. In backlogging systems and lost-sales models with zero lead time, our algorithms adapt to unknown demand changes while matching, up to logarithmic factors, the rates known for the corresponding stationary learning problems. In lost-sales systems with positive lead times, the combination of demand censoring and delayed replenishment restricts counterfactual policy evaluation and leads to weaker regret guarantees. We complement the theoretical analysis with simulation results showing that our methods significantly outperform existing non-oracle benchmarks.

math.OC↗

arXiv2026

Is Pure Exploitation Sufficient in Exogenous MDPs with Linear Function Approximation?

Exogenous MDPs (Exo-MDPs) capture sequential decision-making where uncertainty comes solely from exogenous inputs that evolve independently of the learner's actions. This structure is especially common in operations research applications such as inventory control, energy storage, and resource allocation, where exogenous randomness (e.g., demand, arrivals, or prices) drives system behavior. Despite decades of empirical evidence that greedy, exploitation-only methods work remarkably well in these settings, theory has lagged behind: all existing regret guarantees for Exo-MDPs rely on explicit exploration or tabular assumptions. We show that exploration is unnecessary. We propose Pure Exploitation Learning (PEL) and prove the first general finite-sample regret bounds for exploitation-only algorithms in Exo-MDPs. In the tabular case, PEL achieves $\widetilde{O}(H^2|\Xi|\sqrt{K})$. For large, continuous endogenous state spaces, we introduce LSVI-PE, a simple linear-approximation method whose regret is polynomial in the feature dimension, exogenous state space, and horizon, independent of the endogenous state and action spaces. Our analysis introduces two new tools: counterfactual trajectories and Bellman-closed feature transport, which together allow greedy policies to have accurate value estimates without optimism. Experiments on synthetic and resource-management tasks show that PEL consistently outperforming baselines. Overall, our results overturn the conventional wisdom that exploration is required, demonstrating that in Exo-MDPs, pure exploitation is enough.

cs.LG↗

arXiv2025

Network and Risk Analysis of Surety Bonds

Surety bonds are financial agreements between a contractor (principal) and obligee (project owner) to complete a project. However, most large-scale projects involve multiple contractors, creating a network and introducing the possibility of incomplete obligations to propagate and result in project failures. Typical models for risk assessment assume independent failure probabilities within each contractor. However, we take a network approach, modeling the contractor network as a directed graph where nodes represent contractors and project owners and edges represent contractual obligations with associated financial records. To understand risk propagation throughout the contractor network, we extend the celebrated Friedkin-Johnsen model and introduce a stochastic process to simulate principal failures across the network. From a theoretical perspective, we show that under natural monotonicity conditions on the contractor network, incorporating network effects leads to increases in the average risk for the surety organization. We further use data from a partnering insurance company to validate our findings, estimating an approximately 2% higher exposure when accounting for network effects.

q-fin.RM↗

arXiv2025

Sequential Fair Allocation With Replenishments: A Little Envy Goes An Exponentially Long Way

We study the trade-off between envy and inefficiency in repeated resource allocation settings with stochastic replenishments, motivated by real-world systems such as food banks and medical supply chains. Specifically, we consider a model in which a decision-maker faced with stochastic demand and resource donations must trade off between an equitable and efficient allocation of resources over an infinite horizon. The decision-maker has access to storage with fixed capacity $M$, and incurs efficiency losses when storage is empty (stockouts) or full (overflows). We provide a nearly tight (up to constant factors) characterization of achievable envy-inefficiency pairs. Namely, we introduce a class of Bang-Bang control policies whose inefficiency exhibits a sharp phase transition, dropping from $\Theta(1/M)$ when $\Delta = 0$ to $e^{-\Omega(\Delta M)}$ when $\Delta > 0$, where $\Delta$ is used to denote the target envy of the policy. We complement this with matching lower bounds, demonstrating that the trade-off is driven by supply, as opposed to demand uncertainty. Our results demonstrate that envy-inefficiency trade-offs not only persist in settings with dynamic replenishment, but are shaped by the decision-maker's available capacity, and are therefore qualitatively different compared to previously studied settings with fixed supply.

math.OC↗

arXiv2025

Reinforcement Learning in MDPs with Information-Ordered Policies

We propose an epoch-based reinforcement learning algorithm for infinite-horizon average-cost Markov decision processes (MDPs) that leverages a partial order over a policy class. In this structure, $\pi' \leq \pi$ if data collected under $\pi$ can be used to estimate the performance of $\pi'$, enabling counterfactual inference without additional environment interaction. Leveraging this partial order, we show that our algorithm achieves a regret bound of $O(\sqrt{w \log(|\Theta|) T})$, where $w$ is the width of the partial order. Notably, the bound is independent of the state and action space sizes. We illustrate the applicability of these partial orders in many domains in operations research, including inventory control and queuing systems. For each, we apply our framework to that problem, yielding new theoretical guarantees and strong empirical results without imposing extra assumptions such as convexity in the inventory model or specialized arrival-rate structure in the queuing model.

stat.ML↗

arXiv2024

The Data-Driven Censored Newsvendor Problem

We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than historical demand realizations. Our goal is to understand how the degree of historical demand censoring affects the performance of any learning algorithm for this problem. To isolate this impact, we adopt a distributionally robust optimization framework, evaluating policies according to their worst-case regret over an ambiguity set of distributions. This set is defined by the largest historical order quantity (the observable boundary of the dataset), and contains all distributions matching the true demand distribution up to this boundary, while allowing them to be arbitrary afterwards. We demonstrate a spectrum of achievability under demand censoring by deriving a natural necessary and sufficient condition under which vanishing regret is an achievable goal. In regimes in which it is not, we exactly characterize the information loss due to censoring: an insurmountable lower bound on the performance of any policy, even when the decision-maker has access to infinitely many demand samples. We then leverage these sharp characterizations to propose a natural robust algorithm that adapts to the historical level of demand censoring. We derive finite-sample guarantees for this algorithm across all possible censoring regimes and show its near-optimality with matching lower bounds (up to polylogarithmic factors). We moreover demonstrate its robust performance via extensive numerical experiments on both synthetic and real-world datasets.

math.OC↗

arXiv2024

Exploiting Exogenous Structure for Sample-Efficient Reinforcement Learning

We study a structured class of Markov Decision Processes, known as Exo-MDPs, in which the state space is partitioned into exogenous and endogenous components. Exogenous states evolve stochastically, independent of the agent's actions, while endogenous states evolve deterministically based on both state components and actions. Exo-MDPs capture many operations research settings, including inventory control, resource management, and ride-sharing. Our first contribution is structural: we establish a representational equivalence between discrete MDPs, Exo-MDPs, and discrete linear mixture MDPs. Our second contribution is statistical. We characterize the minimax regret of learning in Exo-MDPs when the effective dimension r is small relative to the endogenous state and action spaces. When the exogenous states are unobserved, we prove matching upper and lower regret bounds of order $\Theta(Hr \sqrt{K})$ over $K$ episodes of horizon $H$, where $r$ is the effective dimension of the Exo-MDP. When exogenous states are observed, the minimax regret improves to $\Theta(H\sqrt{ r K})$, revealing a $\Theta(\sqrt{r})$ statistical gap due to observation of the exogenous states. These results show that Exo-MDPs decouple sample complexity from action space and endogenous state space. We validate these insights with experiments on inventory control and resource allocation.

stat.ML↗

arXiv2024

Multi-Objective LQR with Linear Scalarization

We study finite approximation of the Pareto front for the multi-objective linear quadratic regulator (LQR). Classical results characterize Pareto-optimal controllers through weighted sums of the objectives, but do not quantify the effect of discretizing the scalarization weights. We prove the needed sensitivity property, showing that an $\epsilon$ perturbation of the weights changes the full objective vector by $O(\epsilon)$. Consequently, computing optimal controls over a finite grid of the weight simplex uniformly approximates the Pareto front. We also extend the guarantee to unknown dynamics via certainty equivalence, showing that if the model estimates are accurate to the target accuracy, the same procedure stabilizes the true system and attains the same Pareto-front guarantee.

math.OC↗

arXiv2024

Online Fair Allocation of Perishable Resources

We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and the decision-maker must commit to an allocation for these individuals before moving on to the next round. The goal is to construct a sequence of allocations that is envy-free and efficient. Our work makes two important contributions toward this problem: we first derive strong lower bounds on the optimal envy-efficiency trade-off, demonstrating that a decision-maker is fundamentally limited in what she can hope to achieve relative to the no-perishing setting; we then design an algorithm achieving these lower bounds which takes as input (i) a prediction of the perishing order, and (ii) a desired bound on envy. Given the remaining budget in each period, the algorithm uses forecasts of future demand perishing to adaptively choose from one of two carefully constructed guardrail quantities. We demonstrate our algorithm's strong numerical performance, and state-of-the-art, perishing-agnostic algorithms' inefficacy, on simulations calibrated to a real-world dataset.

math.OC↗

arXiv2022

Artificial Replay: A Meta-Algorithm for Harnessing Historical Data in Bandits

Most real-world deployments of bandit algorithms exist somewhere in between the offline and online set-up, where some historical data is available upfront and additional data is collected dynamically online. How best to incorporate historical data to "warm start" bandit algorithms is an open question: naively initializing reward estimates using all historical samples can suffer from spurious data and imbalanced data coverage, leading to data inefficiency (amount of historical data used) - particularly for continuous action spaces. To address these challenges, we propose ArtificialReplay, a meta-algorithm for incorporating historical data into any arbitrary base bandit algorithm. We show that ArtificialReplay uses only a fraction of the historical data compared to a full warm-start approach, while still achieving identical regret for base algorithms that satisfy independence of irrelevant data (IIData), a novel and broadly applicable property that we introduce. We complement these theoretical results with experiments on K-armed bandits and continuous combinatorial bandits, on which we model green security domains using real poaching data. Our results show the practical benefits of ArtificialReplay for improving data efficiency, including for base algorithms that do not satisfy IIData.

cs.LG↗

arXiv2022

Hindsight Learning for MDPs with Exogenous Inputs

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.

cs.LG↗

arXiv2021

Adaptive Discretization in Online Reinforcement Learning

Discretization based approaches to solving online reinforcement learning problems have been studied extensively in practice on applications ranging from resource allocation to cache management. Two major questions in designing discretization-based algorithms are how to create the discretization and when to refine it. While there have been several experimental results investigating heuristic solutions to these questions, there has been little theoretical treatment. In this paper we provide a unified theoretical analysis of tree-based hierarchical partitioning methods for online reinforcement learning, providing model-free and model-based algorithms. We show how our algorithms are able to take advantage of inherent structure of the problem by providing guarantees that scale with respect to the 'zooming dimension' instead of the ambient dimension, an instance-dependent quantity measuring the benignness of the optimal $Q_h^\star$ function. Many applications in computing systems and operations research requires algorithms that compete on three facets: low sample complexity, mild storage requirements, and low computational burden. Our algorithms are easily adapted to operating constraints, and our theory provides explicit bounds across each of the three facets. This motivates its use in practical applications as our approach automatically adapts to underlying problem structure even when very little is known a priori about the system.

stat.ML↗

arXiv2021

Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve

We consider the problem of dividing limited resources to individuals arriving over $T$ rounds. Each round has a random number of individuals arrive, and individuals can be characterized by their type (i.e. preferences over the different resources). A standard notion of 'fairness' in this setting is that an allocation simultaneously satisfy envy-freeness and efficiency. The former is an individual guarantee, requiring that each agent prefers their own allocation over the allocation of any other; in contrast, efficiency is a global property, requiring that the allocations clear the available resources. For divisible resources, when the number of individuals of each type are known upfront, the above desiderata are simultaneously achievable for a large class of utility functions. However, in an online setting when the number of individuals of each type are only revealed round by round, no policy can guarantee these desiderata simultaneously, and hence the best one can do is to try and allocate so as to approximately satisfy the two properties. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to a factor of $L_T$ necessarily suffers a efficiency loss of at least $1 / L_T$. We complement this uncertainty principle with a simple algorithm, HopeGuardrail, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.

cs.GT↗

arXiv2020

Sequential Fair Allocation of Limited Resources under Stochastic Demands

We consider the problem of dividing limited resources between a set of agents arriving sequentially with unknown (stochastic) utilities. Our goal is to find a fair allocation - one that is simultaneously Pareto-efficient and envy-free. When all utilities are known upfront, the above desiderata are simultaneously achievable (and efficiently computable) for a large class of utility functions. In a sequential setting, however, no policy can guarantee these desiderata simultaneously for all possible utility realizations. A natural online fair allocation objective is to minimize the deviation of each agent's final allocation from their fair allocation in hindsight. This translates into simultaneous guarantees for both Pareto-efficiency and envy-freeness. However, the resulting dynamic program has state-space which is exponential in the number of agents. We propose a simple policy, HopeOnline, that instead aims to `match' the ex-post fair allocation vector using the current available resources and `predicted' histogram of future utilities. We demonstrate the effectiveness of our policy compared to other heurstics on a dataset inspired by mobile food-bank allocations.

cs.GT↗

arXiv2020

Adaptive Discretization for Model-Based Reinforcement Learning

We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces. We illustrate this via experiments on several canonical control problems, which shows that our algorithm empirically performs significantly better than fixed discretization in terms of both faster convergence and lower memory usage. Interestingly, we observe empirically that while fixed-discretization model-based algorithms vastly outperform their model-free counterparts, the two achieve comparable performance with adaptive discretization.

cs.LG↗

arXiv2019

Adaptive Discretization for Episodic Reinforcement Learning in Metric Spaces

We present an efficient algorithm for model-free episodic reinforcement learning on large (potentially continuous) state-action spaces. Our algorithm is based on a novel $Q$-learning policy with adaptive data-driven discretization. The central idea is to maintain a finer partition of the state-action space in regions which are frequently visited in historical trajectories, and have higher payoff estimates. We demonstrate how our adaptive partitions take advantage of the shape of the optimal $Q$-function and the joint space, without sacrificing the worst-case performance. In particular, we recover the regret guarantees of prior algorithms for continuous state-action spaces, which additionally require either an optimal discretization as input, and/or access to a simulation oracle. Moreover, experiments demonstrate how our algorithm automatically adapts to the underlying structure of the problem, resulting in much better performance compared both to heuristics and $Q$-learning with uniform discretization.

cs.LG↗