Worst-case Cost Research Articles

Learning Student Networks with Few Data

Recently, the teacher-student learning paradigm has drawn much attention in compressing neural networks on low-end edge devices, such as mobile phones and wearable watches. Current algorithms mainly assume the complete dataset for the teacher network is also available for the training of the student network. However, for real-world scenarios, users may only have access to part of training examples due to commercial profits or data privacy, and severe over-fitting issues would happen as a result. In this paper, we tackle the challenge of learning student networks with few data by investigating the ground-truth data-generating distribution underlying these few data. Taking Wasserstein distance as the measurement, we assume this ideal data distribution lies in a neighborhood of the discrete empirical distribution induced by the training examples. Thus we propose to safely optimize the worst-case cost within this neighborhood to boost the generalization. Furthermore, with theoretical analysis, we derive a novel and easy-to-implement loss for training the student network in an end-to-end fashion. Experimental results on benchmark datasets validate the effectiveness of our proposed method.

A Linear Programming Approximation of Distributionally Robust Chance-Constrained Dispatch With Wasserstein Distance

This paper proposes a data-driven distributionally robust chance constrained real-time dispatch (DRCC-RTD) considering renewable generation forecasting errors. The proposed DRCC-RTD model minimizes the expected quadratic cost function and guarantees that the two-sided chance constraints are satisfied for any distribution in the ambiguity set. The Wasserstein-distance-based ambiguity set, which is a family of distributions centered at an empirical distribution, is employed to hedge against data perturbations. By applying the reformulation linearization technique (RLT) to relax the quadratic constraints of the worst-case costs and constructing linear reformulations of the DRCCs, the proposed DRCC-RTD model is cast into a deterministic linear programming (LP) problem, which can be solved efficiently by off-the-shelf solvers. Case studies are carried out on a 6-bus system and the IEEE 118-bus system to validate the effectiveness and efficiency of the proposed approach.

On convexity of the robust freeway network control problem in the presence of prediction and model uncertainty

In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging junctions are controlled, there exist tight convex relaxations of the corresponding optimization problem. In practice, many parameters of this optimization problem are not known with certainty, in particular the fundamental diagram and predictions of future traffic demand. This uncertainty poses a challenge for control approaches that pursue a model- and optimization-based strategy. In this work, we propose a robust counterpart to the FNC problem, where we introduce uncertainty sets for both the fundamental diagram and future, external traffic demands and seek to optimize the system operation, minimizing the worst-case cost. For a network with controlled merging junctions, and assuming that certain technical conditions on the uncertainty sets are satisfied, we show that the robust counterpart of the FNC problem can be reduced to a convex, finite-dimensional and deterministic optimization problem, whose numerical solution is tractable.

An exact method for disassembly line balancing problem with limited distributional information

As an important part in product recycling, disassembly line balancing problem (DLBP) has attracted a large amount of attention. Stochastic DLBP is now a hot and challenging research topic, due to its wide applications. This work investigates a DLBP with uncertain task times, where the distributional information is limited, i.e. only the mean values and standard deviations are given, due to the lack of data. From a two-stage perspective, a disassembly process is determined and the disassembly tasks are assigned to workstations in the first stage, and the penalty cost (i.e. the recourse cost) for exceeding the cycle time is minimised in the second stage. The objective is to minimise the expected system cost. For the problem, a two-stage distributionally robust formulation is devised, to minimise the worst-case expected system cost out of all possible probability distributions. Different from literature that focuses on approximation methods to tackle the limited distributional information, an exact method, i.e. the cutting-plane algorithm, is developed. Numerical results show that compared with the state-of-the-art solution methods, our developed cutting-plane algorithm can provide more reliable solutions in term of the robustness, especially in some extreme cases.

Robust Adaptive Model Predictive Control with Worst-Case Cost

Abstract A robust adaptive model predictive control (MPC) algorithm is presented for linear, time invariant systems with unknown dynamics and subject to bounded measurement noise. The system is characterized by an impulse response model, which is assumed to lie within a bounded set called the feasible system set. Online set-membership identification is used to reduce uncertainty in the impulse response. In the MPC scheme, robust constraints are enforced to ensure constraint satisfaction for all the models in the feasible set. The performance objective is formulated as a worst-case cost with respect to the modeling uncertainties. That is, at each time step an optimization problem is solved in which the control input is optimized for the worst-case plant in the uncertainty set. The performance of the proposed algorithm is compared to an adaptive MPC algorithm from the literature using Monte-Carlo simulations.

Formulation of min-max model predictive control as a box-constrained robust least squares estimation problem

The purpose of this paper is to propose a new approach to the Min-Max Model Predictive Control (MMMPC) of Linear Time-Invariant Discrete-time Polytopic (LTIDP) systems. The purpose is to simplify the treatment of complex issues like stability and feasibility analysis of robust MPC as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two Degrees Of Freedom (2DOF) control scheme where the output r(k) of the feedforward Input Estimator (IE) is used as input forcing a stable closed-loop system Σf. Σf is the feedback connection of an LTIDP plant Σp with an LTI dynamic controller Σg. The task of Σg is to guarantee the quadratic stability of Σf, as well as the fulfillment of hard constraints on some physical variables of Σf for any input r(k) satisfying an ”a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on-line minimization of a worst case finite-horizon quadratic cost functional and is applied to Σf according to the usual receding horizon strategy. Rather than resorting to an ”ad hoc” software, the numerical complexity issue is here addressed reducing the number of both decision variables and constraints involved in the on-line constrained optimization procedure. This is obtained modeling r(k) as a B-spline function, which is known to be a universal approximator which also admits a parsimonious parametric representation. This allows us to reformulate the minimization of the worst case cost functional as a box-constrained Robust Least Squares (RLS) estimation problem which can be efficiently solved using Second Order Cone Programming (SOCP).

Worst-case relative cost optimal control for dynamic systems with finite admissible disturbance sequence sets

This paper proposes a controller that gives guaranteed optimal performance in terms of the relative cost for a class of discrete-time nonlinear systems with uncertainties. In some systems, the absolute optimal cost values may be highly dependent on the disturbances. It is desirable to design a controller bounding the relative cost, which is defined as the ratio between the actual cost and the posteriori calculated optimal cost. In this paper, a novel worst-case relative cost optimal control method is developed, assuming that the disturbance sequence belongs to a known finite admissible set. The control policy uses the current states, current accumulated cost, and all current and past disturbance values as feedback. Then the problem is extended to a stochastic case, and the worst-case expected relative cost is minimised. A numerical example on linear systems and a numerical example on the nonlinear hybrid electric vehicle energy management problem are provided.

Robots in the Huddle: Upfront Computation to Reduce Global Communication at Run Time in Multirobot Task Allocation

In this article, we study multirobot task allocation problems where task costs vary. The variation may be, for example, due to the revelation of new information or other dynamic circumstances. As robots update their cost estimates, typically they will update task assignments to reflect the new information using additional communication and computation. In dynamic settings, the robots are continually repairing the optimality of the system's task assignments, which can incur substantial communication and computation. We investigate how one can reduce communication and centralized computation expense during execution by using a prior model of how costs may change and performing upfront computation of possible robot–task assignments. First, we develop an algorithm that partitions a team of robots into several independent subteams that are able to maintain global optimality by communicating entirely amongst themselves. Second, we propose a method for computing the worst-case cost suboptimality if robots persist with the initial assignment and perform no further communication and computation. Finally, we introduce an algorithm to assess whether cost changes affect the optimality of the current assignment through a succession of local communication exchanges. Experimental results show that the proposed methods are helpful in reducing the degree of centralization needed by a multirobot system (e.g., the third method gave at least 45% reduction of global communication across all scenarios studied). The methods are valuable in transitioning multirobot techniques, which have met with success in structured applications (such as factories and warehouses) to the broader, wilder world.

Parallelization of a Common Changepoint Detection Method

In recent years, various means of efficiently detecting changepoints have been proposed, with one popular approach involving minimizing a penalized cost function using dynamic programming. In some situations, these algorithms can have an expected computational cost that is linear in the number of data points; however, the worst case cost remains quadratic. We introduce two means of improving the computational performance of these methods, both based on parallelizing the dynamic programming approach. We establish that parallelization can give substantial computational improvements: in some situations the computational cost decreases roughly quadratically in the number of cores used. These parallel implementations are no longer guaranteed to find the true minimum of the penalized cost; however, we show that they retain the same asymptotic guarantees in terms of their accuracy in estimating the number and location of the changes. Supplementary materials for this article are available online.

확률적 불완전 통신 채널에서의 강인제어

In this paper, we consider the robust (HSUB∞/SUB) control problem for linear time-invariant systems over unreliable communication channels that are subject to packet losses from sensors to the controller and from the controller to the actuators. Moreover, the acknowledgments of control packet transmissions are also sent over reverse unreliable communication channels, which is known as the quasi-TCP model. The robust control problem is formulated within a stochastic zero-sum dynamic game framework, from which we obtain an HSUB∞/SUB controller that minimizes the worst-case cost function in the presence of an adversary in the dynamical system. We characterize a set of existence conditions of the HSUB∞/SUB controller in terms of the disturbance attenuation parameter γ and packet loss rates. For the least disturbance attenuation scenario (γ →∝), we show that the HSUB∞/SUB control system converges to the corresponding LQG system. We also show that the HSUB∞/SUB controller for the TCP- and UDP-cases can be arrived at as appropriate limits of the solution for the quasi-TCP problem. Numerical examples are presented to illustrate the theoretical results.

Learning Robust LQ-Controllers Using Application Oriented Exploration

This letter concerns the problem of learning robust LQ-controllers, when the dynamics of the linear system are unknown. First, we propose a robust control synthesis method to minimize the worst-case LQ cost, with probability 1 - δ, given empirical observations of the system. Next, we propose an approximate dual controller that simultaneously regulates the system and reduces model uncertainty. The objective of the dual controller is to minimize the worst-case cost attained by a new robust controller, synthesized with the reduced model uncertainty. The dual controller is subject to an exploration budget in the sense that it has constraints on its worst-case cost with respect to the current model uncertainty. In our numerical experiments, we observe better performance of the proposed robust LQ regulator over the existing methods. Moreover, the dual control strategy gives promising results in comparison with the common greedy random exploration strategies.

Combining Automated Measurement-Based Cost Modeling With Static Worst-Case Execution-Time and Energy-Consumption Analyses

Predicting the temporal behavior of embedded real-time systems is a crucial but challenging task, as it is with the energetic behavior of energy-constrained systems, such as IoT devices. To carry out static analyses in order to determine the worst-case execution time or the worst-case energy consumption of tasks, cost models are inevitable. However, these models are rarely available on a fine-grained level for commercial-off-the-shelf hardware platforms. In this letter, we present NEO, an end-to-end toolchain that automatically generates cost models, which are then integrated into an existing static-analysis tool. NEO exploits automatically generated benchmark programs, which are measured on the target platform and investigated in a virtual machine. Based on the gathered data, we formulate mathematical optimization problems that eventually yield both worst-case execution-time and energy-consumption cost models. In our evaluations with an embedded hardware platform (e.g., ARM Cortex-M0+), we show that the open-source toolchain is able to precisely bound programs’ resources while achieving acceptable accuracy.

A Game Theoretic Approach to Multi-Period Newsvendor Problems with Censored Markovian Demand

This paper studies the Newsvendor problem for a setting in which (i) the demand is temporally correlated, (ii) the demand is censored, (iii) the distribution of the demand is unknown. The correlation is modeled as a Markovian process. The censoring means that if the demand is larger than the action (selected inventory), only a lower bound on the demand can be revealed. The uncertainty set on the demand distribution is given by only the upper and lower bound on the amount of the change from a time to the next time. We propose a robust approach to minimize the worst-case total cost and model it as a min-max zero-sum repeated game. We prove that the worst-case distribution of the adversary at each time is a two-point distribution with non-zero probabilities at the extrema of the uncertainty set of the demand. And the optimal action of the decision-maker can have any of the following structures: (i) a randomized solution with a two-point distribution at the extrema, (ii) a deterministic solution at a convex combination of the extrema. Both above solutions balance over-utilization and under-utilization costs. Finally, we extend our results to uni-model cost functions and present numerical results to study the solution.

Augmenting Pre-Analysis Plans with Machine Learning

Concerns about the dissemination of spurious results have led to calls for pre-analysis plans (PAPs) to avoid ex-post “p-hacking.” But often the conceptual hypotheses being tested do not imply the level of specificity required for a PAP. In this paper we suggest a framework for PAPs that capitalize on the availability of causal machine-learning (ML) techniques, in which researchers combine specific aspects of the analysis with ML for the flexible estimation of unspecific remainders. A “cheap-lunch” result shows that the inclusion of ML produces limited worst-case costs in power, while offering a substantial upside from systematic specification searches.

Data-Driven Risk-Averse Two-Stage Optimal Stochastic Scheduling of Energy and Reserve With Correlated Wind Power

This paper proposes a data-driven optimization method to solve the integrated energy and reserve dispatch problem with variable and correlated renewable energy generation. The proposed method applies the kernel density estimation to establish an ambiguity set of continuous multivariate probability distributions and the optimization model for the integrated dispatch is formulated as a combination of stochastic and robust optimization problems. First, a risk-averse two-stage stochastic optimization model is formulated to hedge the distributional uncertainty. Next, the second-stage worst case expectation is evaluated, using the equivalent model reformulation, as a combination of conditional value-at-risk (CVaR) and the extreme cost in the worst case scenario. The CVaR is calculated using a scenario-based stochastic optimization problem. After describing the wind power correlation in ellipsoidal uncertainty sets, the robust optimization problem for finding the worst case cost is cast into a mixed-integer second-order cone programming problem. Finally, the column-and-constraint generation method is employed to solve the proposed risk-averse two-stage problem. The proposed method is tested on the 6-bus and IEEE 118-bus systems and validated by comparing the results with those of conventional stochastic and robust optimization methods.

Resilient Configuration Approach of Integrated Community Energy System Considering Integrated Demand Response Under Uncertainty

Integrated community energy system (ICES) enables multi-energy synergy and impulses interaction of integrated demand response (IDR) from the demand side. Nevertheless, the randomness lies in IDR resources and renewable generation in the ICES configuration issue still lacks thorough analysis. Furthermore, the widely focused concern of resiliency urges more proactive consideration of potential emergencies at the planning stage of ICES. To this end, this paper proposed a resilience-oriented stochastic ICES configuration framework considering IDR influence. First, generalized IDR models are set up in detail with elaborate fuzzy feature analysis of price-responsive multi-energy loads. Then, the vulnerability indicators of tie lines and converting devices of the ICES are first introduced to demonstrate the occasional outage in the normal operation and blackout in the emergent case. In addition, the worst-case conditional value-at-risk (WCVaR) theory is innovatively integrated to the traditional risk-neutral model, which is formulated as a two-stage stochastic chance-constrained programming problem, aiming to combine portfolio with minimizing the worst-case cost caused by a disaster. The models are then transformed into mixed-integer linear programming problems via several linearization techniques. Finally, the results of the case studies showed the established model’s superiority in improving the overall economy (reduce 6.94% of the worst-case cost) and system resiliency (decrease the value-at-risk by 3.20%) against an unforeseen hurricane. Meanwhile, the ICES reliability was also improved by declining 25.65% of unintended load curtailment faced with an emergency. The proposed approach provided an efficient preventive portfolio scheme of the IDR-integrated ICES for decision-makers’ different risk preferences of natural hazards.

Solvable integration problems and optimal sample size selection

We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a sample size based on a variance estimation, or – more generally – based on an estimation of a (central absolute) p-moment. That way one can guarantee a small absolute error with high probability, the problem is thus called solvable. The expected cost of the method depends on the p-moment of the random variable, which can be arbitrarily large. In order to prove the optimality of our algorithm we also provide lower bounds. These bounds apply not only to methods based on i.i.d. samples but also to general randomized algorithms. They show that – up to constants – the cost of the algorithm is optimal in terms of accuracy, confidence level, and norm of the particular input random variable. Since the considered classes of random variables or integrands are very large, the worst case cost would be infinite. Nevertheless one can define adaptive stopping rules such that for each input the expected cost is finite. We contrast these positive results with examples of integration problems that are not solvable.

A parallel branch-and-bound algorithm to compute a tighter tardiness bound for preemptive global EDF

In this paper we present a parallel exact algorithm to compute an upper bound to tardiness of preemptive global EDF (G-EDF) schedulers, named harmonic bound, which has been proved to be up to 30% tighter than previously proposed bounds. Tightness is a crucial property of tardiness bounds: a too loose bound may cause a feasible soft real-time application to be mistakenly deemed unfeasible. Unfortunately, no polynomial-time algorithm is known to date to compute the harmonic bound. Although there is no proof of hardness of any sort either, the complex formula of the bound apparently provides no hints to devise algorithms with sub-exponential worst-case cost. In this paper we address this issue by proposing a parallel, exact, branch-and-bound algorithm to compute the harmonic bound, called harm-BB, which proves to be extremely fast in a large number of experiments. More specifically, we compare its execution times with those of existing polynomial-time algorithms for other known tardiness bounds on 630,000 random task sets. harm-BB outperforms, or is comparable to, the competitor algorithms in all scenarios but the ones with the highest number of processors (7 and 8) and tasks ( $$\sim $$ 50). In the latter scenarios harm-BB is indeed slower than the other algorithms; yet, it was still feasible, as it takes only about 2.8 s to compute the bound on a commodity dual-core CPU. Even better, we show that harm-BB has a high parallel efficiency, thus its execution time may be largely cut down on highly-parallel platforms.

Worst-case bounds and optimized cache on [formula omitted]th request cache insertion policies under elastic conditions

Cloud services and other shared third-party infrastructures allow individual content providers to easily scale their services based on current resource demands. In this paper, we consider an individual content provider that wants to minimize its delivery costs under the assumptions that the storage and bandwidth resources it requires are elastic, the content provider only pays for the resources that it consumes, and costs are proportional to the resource usage. Within this context, we (i) derive worst-case bounds for the optimal cost and competitive cost ratios of different classes of cache onMth request cache insertion policies, (ii) derive explicit average cost expressions and bounds under arbitrary inter-request distributions, (iii) derive explicit average cost expressions and bounds for short-tailed (deterministic, Erlang, and exponential) and heavy-tailed (Pareto) inter-request distributions, and (iv) present numeric and trace-based evaluations that reveal insights into the relative cost performance of the policies. Our results show that a window-based cache on 2nd request policy using a single threshold optimized to minimize worst-case costs provides good average performance across the different distributions and the full parameter ranges of each considered distribution, making it an attractive choice for a wide range of practical conditions where request rates of individual file objects typically are not known and can change quickly.

A selfish allocation heuristic in scheduling: Equilibrium and inefficiency bound analysis

For single decision maker optimization problems that lack time efficient algorithms to determine the optimum, there is a need for heuristics. In the context of coordinated production planning, the seminal paper of Graham (1969) provided a performance analysis of heuristics and obtained a bound in relation to the centralized optimum.This paper introduces a framework that includes a performance analysis of a so-called equilibrium heuristic in the setting of multiple decision maker problems. The framework consists of three steps: a heuristic for each player that leads to a strategy profile, the verification that this strategy profile is a Nash equilibrium, and finally a worst case cost analysis to obtain a bound on the performance of the heuristic in terms of the aggregate cost in the obtained Nash equilibrium in relation to the centralized optimum.We implement our general framework in a setting of sequencing situations with selfish agents, multiple identical machines, and the sum of completion times as cost criterion. We provide a tight upper bound for the performance of our equilibrium heuristic. Simulations show that the equilibrium heuristic generally performs much better than the derived tight upper bound. Finally, the relation with the price of anarchy is discussed.