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Register a new userA Complete Algebraic Solution to the Optimal Dynamic Rationing Policy in the Stock-Rationing Queue with Two Demand Classes
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Quan-Lin Li
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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In this paper, we study a stock-rationing queue with two demand classes by means of the sensitivity-based optimization, and develop a complete algebraic solution to the optimal dynamic rationing policy. We show that the optimal dynamic rationing policy must be of transformational threshold type. Based on this finding, we can refine three sufficient conditions under each of which the optimal dynamic rationing policy is of threshold type (i.e., critical rationing level). To do this, we use the performance difference equation to characterize the monotonicity and optimality of the long-run average profit of this system, and thus establish some new structural properties of the optimal dynamic rationing policy by observing any given reference policy. Finally, we use numerical experiments to demonstrate our theoretical results of the optimal dynamic rationing policy. We believe that the methodology and results developed in this paper can shed light on the study of stock-rationing queues and open a series of potentially promising research.
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We study the allocative challenges that governmental and nonprofit organizations face when tasked with equitable and efficient rationing of a social good among agents whose needs (demands) realize sequentially and are possibly correlated. To better achieve their dual aims of equity and efficiency in such contexts, social planners intend to maximize the minimum fill rate across agents, where each agents fill rate must be irrevocably decided upon its arrival. For an arbitrarily correlated sequence of demands, we establish upper bounds on both the expected minimum fill rate (ex-post fairness) and the minimum expected fill rate (ex-ante fairness) achievable by any policy. Our bounds are parameterized by the number of agents and the expected demand-to-supply ratio, and they shed light on the limits of attaining equity in dynamic rationing. Further, we show that for any set of parameters, a simple adaptive policy of projected proportional allocation achieves the best possible fairness guarantee, ex post as well as ex ante. Our policy is transparent and easy to implement; yet despite its simplicity, we demonstrate that this policy provides significant improvement over the class of non-adaptive target-fill-rate policies. We obtain the performance guarantees of (i) our proposed adaptive policy by inductively designing lower-bound functions on its corresponding value-to-go, and (ii) the optimal target-fill-rate policy by establishing an intriguing connection to a monopoly-pricing optimization problem. We complement our theoretical developments with a numerical study motivated by the rationing of COVID-19 medical supplies based on a projected-demand model used by the White House. In such a setting, our simple adaptive policy significantly outperforms its theoretical guarantee as well as the optimal target-fill-rate policy.
In this paper, we introduce a model of dynamical queue, in which the service time depends on the server utilization history. The proposed queueing model is motivated by widely accepted empirical laws describing human performance as a function of mental arousal. The objective of this paper is to design task release control policies that can stabilize the queue for the maximum possible arrival rate, assuming deterministic arrivals. First, we prove an upper bound on the maximum possible stabilizable arrival rate for any task release control policy. Then, we propose a simple threshold policy that releases a task to the server only if its state is below a certain fixed value. Finally, we prove that this task release control policy ensures stability of the queue for the maximum possible arrival rate.
We advocate a new resource allocation framework, which we term resource rationing, for wireless federated learning (FL). Unlike existing resource allocation methods for FL, resource rationing focuses on balancing resources across learning rounds so that their collective impact on the federated learning performance is explicitly captured. This new framework can be integrated seamlessly with existing resource allocation schemes to optimize the convergence of FL. In particular, a novel later-is-better principle is at the front and center of resource rationing, which is validated empirically in several instances of wireless FL. We also point out technical challenges and research opportunities that are worth pursuing. Resource rationing highlights the benefits of treating the emerging FL as a new class of service that has its own characteristics, and designing communication algorithms for this particular service.
This paper characterizes the solution to a finite horizon min-max optimal control problem where the system is linear and discrete-time with control and state constraints, and the cost quadratic; the disturbance is negatively costed, as in the standard H-infinity problem, and is constrained. The cost is minimized over control policies and maximized over disturbance sequences so that the solution yields a feedback control. It is shown that the value function is piecewise quadratic and the optimal control policy piecewise affine, being quadratic and affine, respectively, in polytopes that partition the domain of the value function.
Successful quantitative investment usually relies on precise predictions of the future movement of the stock price. Recently, machine learning based solutions have shown their capacity to give more accurate stock prediction and become indispensable components in modern quantitative investment systems. However, the i.i.d. assumption behind existing methods is inconsistent with the existence of diverse trading patterns in the stock market, which inevitably limits their ability to achieve better stock prediction performance. In this paper, we propose a novel architecture, Temporal Routing Adaptor (TRA), to empower existing stock prediction models with the ability to model multiple stock trading patterns. Essentially, TRA is a lightweight module that consists of a set of independent predictors for learning multiple patterns as well as a router to dispatch samples to different predictors. Nevertheless, the lack of explicit pattern identifiers makes it quite challenging to train an effective TRA-based model. To tackle this challenge, we further design a learning algorithm based on Optimal Transport (OT) to obtain the optimal sample to predictor assignment and effectively optimize the router with such assignment through an auxiliary loss term. Experiments on the real-world stock ranking task show that compared to the state-of-the-art baselines, e.g., Attention LSTM and Transformer, the proposed method can improve information coefficient (IC) from 0.053 to 0.059 and 0.051 to 0.056 respectively. Our dataset and code used in this work are publicly available: https://github.com/microsoft/qlib/tree/main/examples/benchmarks/TRA.
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