The Bayesian Prophet: A Low-Regret Framework for Online Decision Making

We develop a new framework for designing online policies given access to an oracle providing statistical information about an off-line benchmark. Having access to such prediction oracles enables simple and natural Bayesian selection policies and raises the question as to how these policies perform in different settings. Our work makes two important contributions toward this question: First, we develop a general technique we call compensated coupling, which can be used to derive bounds on the expected regret (i.e., additive loss with respect to a benchmark) for any online policy and off-line benchmark. Second, using this technique, we show that a natural greedy policy, which we call the Bayes selector, has constant expected regret (i.e., independent of the number of arrivals and resource levels) for a large class of problems we refer to as “online allocation with finite types,” which includes widely studied online packing and online matching problems. Our results generalize and simplify several existing results for online packing and online matching and suggest a promising pathway for obtaining oracle-driven policies for other online decision-making settings. This paper was accepted by George Shanthikumar, big data analytics.

Computing a Pessimistic Stackelberg Equilibrium with Multiple Followers: The Mixed-Pure Case

The search problem of computing a Stackelberg (or leader-follower)equilibrium (also referred to as an optimal strategy to commit to) has been widely investigated in the scientific literature in, almost exclusively, the single-follower setting. Although the optimistic and pessimistic versions of the problem, i.e., those where the single follower breaks any ties among multiple equilibria either in favour or against the leader, are solved with different methodologies, both cases allow for efficient, polynomial-time algorithms based on linear programming. The situation is different with multiple followers, where results are only sporadic and depend strictly on the nature of the followers’ game. In this paper, we investigate the setting of a normal-form game with a single leader and multiple followers who, after observing the leader’s commitment, play a Nash equilibrium. When both leader and followers are allowed to play mixed strategies, the corresponding search problem, both in the optimistic and pessimistic versions, is known to be inapproximable in polynomial time to within any multiplicative polynomial factor unless $$\textsf {P}=\textsf {NP}$$P=NP. Exact algorithms are known only for the optimistic case. We focus on the case where the followers play pure strategies—a restriction that applies to a number of real-world scenarios and which, in principle, makes the problem easier—under the assumption of pessimism (the optimistic version of the problem can be straightforwardly solved in polynomial time). After casting this search problem (with followers playing pure strategies) as a pessimistic bilevel programming problem, we show that, with two followers, the problem is -hard and, with three or more followers, it cannot be approximated in polynomial time to within any multiplicative factor which is polynomial in the size of the normal-form game, nor, assuming utilities in [0, 1], to within any constant additive loss stricly smaller than 1 unless $$\textsf {P}=\textsf {NP}$$P=NP. This shows that, differently from what happens in the optimistic version, hardness and inapproximability in the pessimistic problem are not due to the adoption of mixed strategies. We then show that the problem admits, in the general case, a supremum but not a maximum, and we propose a single-level mathematical programming reformulation which asks for the maximization of a nonconcave quadratic function over an unbounded nonconvex feasible region defined by linear and quadratic constraints. Since, due to admitting a supremum but not a maximum, only a restricted version of this formulation can be solved to optimality with state-of-the-art methods, we propose an exact ad hoc algorithm (which we also embed within a branch-and-bound scheme) capable of computing the supremum of the problem and, for cases where there is no leader’s strategy where such value is attained, also an $$\alpha $$α-approximate strategy where $$\alpha > 0$$α>0 is an arbitrary additive loss (at most as large as the supremum). We conclude the paper by evaluating the scalability of our algorithms via computational experiments on a well-established testbed of game instances.

Actuator Fault Sensitivity Analysis for In-Wheel Motor Electric Ground Vehicle With Active Steering System

This paper presents the sensitivity analyses on vehicle motions with regard to faults of in-wheel motors and steering motor for an electric ground vehicle (EGV) with independently actuated in-wheel rear motors. Based on the vehicle model, direct method is applied to determine, to what extent, that different actuator faults affect vehicle motions such as the longitudinal velocity, lateral velocity, and yaw rate. For motion indices like vehicle sideslip angle and longitudinal acceleration, linearizations around equilibrium points are conducted and their sensitivities to actuator faults are analyzed. Results show that all mentioned vehicle motions are more sensitive to the fault of steering motor than that of in-wheel motors. In addition, the effects on vehicle motions due to four types of faults, i.e. additive, loss-of-effectiveness, time-varying-gain and stuck-at-fixed-level faults, are examined through CarSim® simulations and vehicle experiments under a representative maneuver.

Effects of Reprocessing on Additives in ABS Plastics, Detected by Gas Chromatography/Mass Spectrometry

Acrylonitrile–butadiene–styrene (ABS) plastic is a widely used engineering thermoplastic. ABS is also an interesting material for recycling. In the present study, two pieces of ABS plastic from waste computer equipment were reprocessed. A torque rheometer was used to simulate reprocessing. To identify the additives used in the recycled ABS plastics and understand the effect of reprocessing on the recycled plastics from several aspects, gas chromatography/mass spectrometry (GC/MS) was used to analyse the extracts from recycled ABS plastics before and after reprocessing. The effects of reprocessing temperature and reprocessing cycle on some additives, mainly antioxidants and lubricants, were investigated. Plastic processing led to additive loss because of volatilisation, decomposition, or conversion, particularly at high temperatures and during multiple processing cycles.