Contract scheduling is a widely studied framework for designing real-time systems with interruptible capabilities. Previous work has showed that a prediction on the interruption time can help improve the performance of contract-based systems, however it has relied on a single prediction that is provided by a deterministic oracle. In this work, we introduce and study more general and realistic learning-augmented settings in which the prediction is in the form of a probability distribution, or it is given as a set of multiple possible interruption times. For both prediction settings, we design and analyze schedules which perform optimally if the prediction is accurate, while simultaneously guaranteeing the best worst-case performance if the prediction is adversarial. We also provide evidence that the resulting system is robust to prediction errors in the distributional setting. Last, we present an experimental evaluation that confirms the theoretical findings, and illustrates the performance improvements that can be attained in practice.

Contract scheduling is a general technique that allows the design of systems with interruptible capabilities, given an algorithm that is not necessarily interruptible. Previous work on this topic has assumed that the interruption is a worst-case deadline that is unknown to the scheduler. In this work, we study new settings in which the scheduler has access to some imperfect prediction in regards to the interruption. In the first setting, which is inspired by recent advances in learning-enhanced algorithms, the prediction describes the time that the interruption occurs. The second setting introduces a new model in which predictions are elicited as responses to a number of binary queries. For both settings, we investigate trade-offs between the robustness (i.e., the worst-case performance of the schedule if the prediction is generated adversarially) and the consistency (i.e., the performance assuming that the prediction is error-free). We also establish results on the performance of the schedules as a function of the prediction error.

Contract scheduling is a general technique that allows to design a system with interruptible capabilities, given an algorithm that is not necessarily interruptible. Previous work on this topic has largely assumed that the interruption is a worst-case deadline that is unknown to the scheduler. In this work, we study the setting in which there is a potentially erroneous prediction concerning the interruption. Specifically, we consider the setting in which the prediction describes the time that the interruption occurs, as well as the setting in which the prediction is obtained as a response to a single or multiple binary queries. For both settings, we investigate tradeoffs between the robustness (i.e., the worst-case performance assuming adversarial prediction) and the consistency (i.e, the performance assuming that the prediction is error-free), both from the side of positive and negative results.

In this paper we address the problem of designing an interruptible system in a setting in which $n$ problem instances, all equally important, must be solved concurrently. The system involves scheduling executions of contract algorithms (which offer a trade-off between allowable computation time and quality of the solution) in m identical parallel processors. When an interruption occurs, the system must report a solution to each of the $n$ problem instances. The quality of this output is then compared to the best-possible algorithm that has foreknowledge of the interruption time and must, likewise, produce solutions to all $n$ problem instances. This extends the well-studied setting in which only one problem instance is queried at interruption time. In this work we first introduce new measures for evaluating the performance of interruptible systems in this setting. In particular, we propose the deficiency of a schedule as a performance measure that meets the requirements of the problem at hand. We then present a schedule whose performance we prove that is within a small factor from optimal in the general, multiprocessor setting. We also show several lower bounds on the deficiency of schedules on a single processor. More precisely, we prove a general lower bound of (n+1)/n, an improved lower bound for the two-problem setting (n=2), and a tight lower bound for the class of round-robin schedules. Our techniques can also yield a simpler, alternative proof of the main result of [Bernstein et al, IJCAI 2003] concerning the performance of cyclic schedules in multiprocessor environments.

Anytime algorithms give intelligent systems the capability to trade deliberation time for quality of results. This capability is essential for successful operation in domains such as signal interpretation, real-time diagnosis and repair, and mobile robot control. What characterizes these domains is that it is not feasible (computationally) or desirable (economically) to compute the optimal answer. This article surveys the main control problems that arise when a system is composed of several anytime algorithms. These problems relate to optimal management of uncertainty and precision. After a brief introduction to anytime computation, I outline a wide range of existing solutions to the metalevel control problem and describe current work that is aimed at increasing the applicability of anytime computation. The term anytime algorithm was coined by Dean and Boddy in the mid-1980s in the context of their work on time-dependent planning (Dean and Boddy 1988; Dean 1987).

This paper addresses two classes of different, yet interrelated optimization problems. The first class of problems involves a robot that must locate a hidden target in an environment that consists of a set of concurrent rays. The second class pertains to the design of interruptible algorithms by means of a schedule of contract algorithms. We study several variants of these families of problems, such as searching and scheduling with probabilistic considerations, redundancy and fault-tolerance issues, randomized strategies, and trade-offs between performance and preemptions. For many of these problems we present the first known results that apply to multi-ray and multi-problem domains. Our objective is to demonstrate that several well-motivated settings can be addressed using a common approach.

A contract algorithm is an algorithm which is given, as part of the input, a specified amount of allowable computation time. The algorithm must then complete its execution within the allotted time. An interruptible algorithm, in contrast, can be interrupted at an arbitrary point in time, at which point it must report its currently best solution. It is known that contract algorithms can simulate interruptible algorithms using iterative deepening techniques. This simulation is done at a penalty in the performance of the solution, as measured by the so-called acceleration ratio. In this paper we give matching (i.e., optimal) upper and lower bounds for the acceleration ratio under such a simulation. We assume the most general setting in which n problem instances must be solved by means of scheduling executions of contract algorithms in $m$ identical parallel processors. This resolves an open conjecture of Bernstein, Filkenstein, and Zilberstein who gave an optimal schedule under the restricted setting of round robin and length-increasing schedules, but whose optimality in the general unrestricted case remained open. Lastly, we show how to evaluate the average acceleration ratio of the class of exponential strategies in the setting of n problem instances and m parallel processors. This is a broad class of schedules that tend to be either optimal or near-optimal, for several variants of the basic problem.

In this paper we address the problem of designing an interruptible system in a setting in which n problem instances, all equally important, must be solved. The system involves  scheduling executions of contract algorithms (which offer a trade-off between allowable computation time and quality of the solution) in m identical parallel processors. When an interruption occurs, the system must report a solution to each of the n problem instances. The quality of this output is then compared to the best-possible algorithm that has foreknowledge of the interruption time and must, likewise, produce solutions to all n problem instances. This extends the well-studied setting in which only one problem instance is queried at interruption time. We propose a schedule which we prove is optimal for the case of a single processor. For multiple processors, we show that the quality of the schedule is within a small factor from optimal.

Anytime algorithms give intelligent systems the capability to trade deliberation time for quality of results. This capability is essential for successful operation in domains such as signal interpretation, real-time diagnosis and repair, and mobile robot control. What characterizes these domains is that it is not feasible (computationally) or desirable (economically) to compute the optimal answer. This article surveys the main control problems that arise when a system is composed of several anytime algorithms. These problems relate to optimal management of uncertainty and precision. After a brief introduction to anytime computation, I outline a wide range of existing solutions to the metalevel control problem and describe current work that is aimed at increasing the applicability of anytime computation.