An official website of the United States government
In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule jobs with time-varying resource requirements is limited. Motivated by this gap, we propose a new setting of the stochastic bin-packing problem in service systems that allows for time-varying job resource requirements, also referred to as 'item sizes' in traditional bin-packing terms. In this setting, a job or 'item' must be dispatched to a server or 'bin' upon arrival. Its resource requirement may vary over time while in service, following a Markovian assumption. Once the job's service is complete, it departs from the system. Our goal is to minimize the expected number of active servers, or 'non-empty bins', in steady state. Under our problem formulation, we develop a job dispatch policy, named Join-Reqesting-Server (JRS). Broadly, JRS lets each server independently evaluate its current job configuration and decide whether to accept additional jobs, balancing the competing objectives of maximizing throughput and minimizing the risk of resource capacity overruns. The JRS dispatcher then utilizes these individual evaluations to decide which server to dispatch each arriving job to. The theoretical performance guarantee of JRS is in the asymptotic regime where the job arrival rate scales large linearly with respect to a scaling factor r. We show that JRS achieves an additive optimality gap of O(√r) in the objective value, where the optimal objective value is Θ(r). When specialized to constant job resource requirements, our result improves upon the state-of-the-art o(r) optimality gap. Our technical approach highlights a novel policy conversion framework that reduces the policy design problem into a single-server problem.
more »
« less
Restless Bandits with Average Reward: Breaking the Uniform Global Attractor Assumption
We study the infinite-horizon Restless Bandit problem with the average reward criterion, under both discrete-time and continuous-time settings. A fundamental goal is to design computationally efficient policies that achieve a diminishing optimality gap as the number of arms, N, grows large. Existing results on asymptotic optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. In this paper, we propose a general, simulation-based framework, Follow-the-Virtual-Advice, that converts any single-armed policy into a policy for the original N-armed problem. This is done by simulating the single-armed policy on each arm and carefully steering the real state towards the simulated state. Our framework can be instantiated to produce a policy with an O(1/pN) optimality gap. In the discrete-time setting, our result holds under a simpler synchronization assumption, which covers some problem instances that violate UGAP. More notably, in the continuous-time setting, we do not require any additional assumptions beyond the standard unichain condition. In both settings, our work is the first asymptotic optimality result that does not require UGAP.
more »
« less
- Award ID(s):
- 2007733
- PAR ID:
- 10486826
- Publisher / Repository:
- NeurIPS Proceedings
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)We study the deadline scheduling problem for multiple deferrable jobs that arrive in a random manner and are to be processed before individual deadlines. The processing of the jobs is subject to a time-varying limit on the total processing rate at each stage. We formulate the scheduling problem as a restless multi-armed bandit (RMAB) problem. Relaxing the scheduling problem into multiple independent single-arm scheduling problems, we define the Lagrangian priority value as the greatest tax under which it is optimal to activate the arm, and establish the asymptotic optimality of the proposed Lagrangian priority policy for large systems. Numerical results show that the proposed Lagrangian priority policy achieves 22%-49% higher average reward than the classical Whittle index policy (that does not take into account the processing rate limits).more » « less
-
null (Ed.)We study the problem of learning sequential decision-making policies in settings with multiple state-action representations. Such settings naturally arise in many domains, such as planning (e.g., multiple integer programming formulations) and various combinatorial optimization problems (e.g., those with both integer programming and graph-based formulations). Inspired by the classical co-training framework for classification, we study the problem of co-training for policy learning. We present sufficient conditions under which learning from two views can improve upon learning from a single view alone. Motivated by these theoretical insights, we present a meta-algorithm for co-training for sequential decision making. Our framework is compatible with both reinforcement learning and imitation learning. We validate the effectiveness of our approach across a wide range of tasks, including discrete/continuous control and combinatorial optimization.more » « less
-
Adams, RP; Gogate V (Ed.)We study the problem of learning sequential decision-making policies in settings with multiple state-action representations. Such settings naturally arise in many domains, such as planning (e.g., multiple integer programming formulations) and various combinatorial optimization problems (e.g., those with both integer programming and graph-based formulations). Inspired by the classical co-training framework for classification, we study the problem of co-training for policy learning. We present sufficient conditions under which learning from two views can improve upon learning from a single view alone. Motivated by these theoretical insights, we present a meta-algorithm for co-training for sequential decision making. Our framework is compatible with both reinforcement learning and imitation learning. We validate the effectiveness of our approach across a wide range of tasks, including discrete/continuous control and combinatorial optimization.more » « less
-
We consider the problem of scheduling to minimize asymptotic tail latency in an M/G/1 queue with unknown job sizes. When the job size distribution is heavy-tailed, numerous policies that do not require job size information (e.g. Processor Sharing, Least Attained Service) are known to be strongly tail optimal, meaning that their response time tail has the fastest possible asymptotic decay. In contrast, for light-tailed size distributions, only in the last few years have policies been developed that outperform simple First-Come First-Served (FCFS). The most recent of these is γ-Boost, which achieves strong tail optimality in the light-tailed setting. But thus far, all policies that outperform FCFS in the light-tailed setting, including γ-Boost, require known job sizes. In this paper, we design a new scheduling policy that achieves strong tail optimality in the light-tailed M/G/1 with unknown job sizes. Surprisingly, the optimal policy turns out to be a variant of the Gittins policy, but with a novel and unusual feature: it uses a negative discount rate. Our work also applies to systems with partial information about job sizes, covering γ-Boost as an extreme case when job sizes are in fact fully known.more » « less
