Performance Guarantees Research Articles

SunPeek Open-Source Software for ISO 24194 Performance Assessment and Monitoring of Large-Scale Solar Thermal Plants

ISO 24194:2022, the first standard specifically designed to assess the operational performance of solar thermal collector arrays, is likely to have substantial impact on the entire solar thermal industry. This standard introduces the Power Check, a method that can be used for monitoring ongoing plant operation and for checking performance guarantees. However, its practical use is presently limited, as initial applications indicate a need for clarification, and it exists as a mere paper description, rendering it less accessible for plant designers and operators. Furthermore, any implementation necessitates practical decisions regarding data handling and algorithm implementation. Closed-source implementations, lacking a traceable and transparent framework, could lead to inconsistent results. To address these issues, this paper introduces SunPeek, an open-source software that provides a reference implementation of the ISO 24194 Power Check. SunPeek is freely accessible for both scientific and commercial purposes. This paper also discusses existing limitations of ISO 24194 and showcases five examples of SunPeek applied to real-life solar thermal plants. This underscores potential practical challenges, such as handling stagnation events, and highlights methodological progress, such as improved data filtering for performance analyses. The findings and applications indicate SunPeek’s usability and the high potential for ISO 24194-based performance monitoring of solar thermal plants.

Virtual control contraction metrics: Convex nonlinear feedback design via behavioral embedding

AbstractThis article presents a systematic approach to nonlinear state‐feedback control design that has three main advantages: (i) it ensures exponential stability and ‐gain performance with respect to a user‐defined set of reference trajectories, (ii) it provides constructive conditions based on convex optimization and a path‐integral‐based control realization, and (iii) it is less restrictive than previous similar approaches. In the proposed approach, first a virtual representation of the nonlinear dynamics is constructed for which a behavioral (parameter‐varying) embedding is generated. Then, by introducing a virtual control contraction metric, a convex control synthesis formulation is derived. Finally, a control realization with a virtual reference generator is computed, which is guaranteed to achieve exponential stability and ‐gain performance for all trajectories of the targeted reference behavior. We show that the proposed methodology is a unified generalization of the two distinct categories of linear‐parameter‐varying (LPV) state‐feedback control approaches: global and local methods. Moreover, it provides rigorous stability and performance guarantees as a method for nonlinear tracking control, while such properties are not guaranteed for tracking control using standard LPV approaches. Code is available at https://github.com/ruigangwang7/VCCM.

Offline Planning and Online Learning Under Recovering Rewards

Motivated by emerging applications, such as live-streaming e-commerce, promotions, and recommendations, we introduce and solve a general class of nonstationary multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from up to [Formula: see text] out of N different arms in each time period and (ii) the expected reward of an arm immediately drops after it is pulled and then nonparametrically recovers as the arm’s idle time increases. With the objective of maximizing the expected cumulative reward over T time periods, we design a class of purely periodic policies that jointly set a period to pull each arm. For the proposed policies, we prove performance guarantees for both the offline and the online problems. For the offline problem when all model parameters are known, the proposed periodic policy obtains a long-run approximation ratio that is at the order of [Formula: see text], which is asymptotically optimal when K grows to infinity. For the online problem when the model parameters are unknown and need to be dynamically learned, we integrate the offline periodic policy with the upper confidence bound procedure to construct on online policy. The proposed online policy is proved to approximately have [Formula: see text] regret against the offline benchmark. Our framework and policy design may shed light on broader offline planning and online learning applications with nonstationary and recovering rewards. This paper was accepted by J. George Shanthikumar, data science. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.04202 .

P2BPO: Permeable Penalty Barrier-Based Policy Optimization for Safe RL

Safe Reinforcement Learning (SRL) algorithms aim to learn a policy that maximizes the reward while satisfying the safety constraints. One of the challenges in SRL is that it is often difficult to balance the two objectives of reward maximization and safety constraint satisfaction. Existing algorithms utilize constraint optimization techniques like penalty-based, barrier penalty-based, and Lagrangian-based dual or primal policy optimizations methods. However, they suffer from training oscillations and approximation errors, which impact the overall learning objectives. This paper proposes the Permeable Penalty Barrier-based Policy Optimization (P2BPO) algorithm that addresses this issue by allowing a small fraction of penalty beyond the penalty barrier, and a parameter is used to control this permeability. In addition, an adaptive penalty parameter is used instead of a constant one, which is initialized with a low value and increased gradually as the agent violates the safety constraints. We have also provided a theoretical proof of the proposed method's performance guarantee bound, which ensures that P2BPO can learn a policy satisfying the safety constraints with high probability while achieving a higher expected reward. Furthermore, we compare P2BPO with other SRL algorithms on various SRL tasks and demonstrate that it achieves better rewards while adhering to the constraints.

A Fast Exact Solver with Theoretical Analysis for the Maximum Edge-Weighted Clique Problem

The maximum vertex-weighted clique problem (MVWCP) and the maximum edge-weighted clique problem (MEWCP) are two natural extensions of the fundamental maximum clique problem. In this paper, we systematically study MEWCP and make the following major contributions: (1) We show that MEWCP is NP-hard even when the minimum degree of the graph is n-2, in contrast to MVWCP which is polynomial-time solvable when the minimum degree of the graph is at least n-3. This result distinguishes the complexity of the two problems for the first time. (2) To address MEWCP, we develop an efficient branch-and-bound algorithm called MEWCat with both practical and theoretical performance guarantees. In practice, MEWCat utilizes a new upper bound tighter than existing ones, which allows for more efficient pruning of branches. In theory, we prove a running-time bound of O*(1.4423^n) for MEWCat, which breaks the trivial bound of O*(2^n) in the research line of practical exact MEWCP solvers for the first time. (3) Empirically, we evaluate the performance of MEWCat on various benchmark instances. The experiments demonstrate that MEWCat outperforms state-of-the-art exact solvers significantly. For instance, on 16 DIMACS graphs that the state-of-the-art solver BBEWC fails to solve within 7200 seconds, MEWCat solves all of them with an average time of less than 1000 seconds. On real-world graphs, MEWCat achieves an average speedup of over 36x.

Dynamic Knowledge Injection for AIXI Agents

Prior approximations of AIXI, a Bayesian optimality notion for general reinforcement learning, can only approximate AIXI's Bayesian environment model using an a-priori defined set of models. This is a fundamental source of epistemic uncertainty for the agent in settings where the existence of systematic bias in the predefined model class cannot be resolved by simply collecting more data from the environment. We address this issue in the context of Human-AI teaming by considering a setup where additional knowledge for the agent in the form of new candidate models arrives from a human operator in an online fashion. We introduce a new agent called DynamicHedgeAIXI that maintains an exact Bayesian mixture over dynamically changing sets of models via a time-adaptive prior constructed from a variant of the Hedge algorithm. The DynamicHedgeAIXI agent is the richest direct approximation of AIXI known to date and comes with good performance guarantees. Experimental results on epidemic control on contact networks validates the agent's practical utility.

Learning-Augmented Online Algorithm for Two-Level Ski-Rental Problem

In this paper, we study the two-level ski-rental problem, where a user needs to fulfill a sequence of demands for multiple items by choosing one of the three payment options: paying for the on-demand usage (i.e., rent), buying individual items (i.e., single purchase), and buying all the items (i.e., combo purchase). Without knowing future demands, the user aims to minimize the total cost (i.e., the sum of the rental, single purchase, and combo purchase costs) by balancing the trade-off between the expensive upfront costs (for purchase) and the potential future expenses (for rent). We first design a robust online algorithm (RDTSR) that offers a worst-case performance guarantee. While online algorithms are robust against the worst-case scenarios, they are often overly cautious and thus suffer a poor average performance in typical scenarios. On the other hand, Machine Learning (ML) algorithms typically show promising average performance in various applications but lack worst-case performance guarantees. To harness the benefits of both methods, we develop a learning-augmented algorithm (LADTSR) by integrating ML predictions into the robust online algorithm, which outperforms the robust online algorithm under accurate predictions while ensuring worst-case performance guarantees even when predictions are inaccurate. Finally, we conduct numerical experiments on both synthetic and real-world trace data to corroborate the effectiveness of our approach.

Factorized Explainer for Graph Neural Networks

Graph Neural Networks (GNNs) have received increasing attention due to their ability to learn from graph-structured data. To open the black-box of these deep learning models, post-hoc instance-level explanation methods have been proposed to understand GNN predictions. These methods seek to discover substructures that explain the prediction behavior of a trained GNN. In this paper, we show analytically that for a large class of explanation tasks, conventional approaches, which are based on the principle of graph information bottleneck (GIB), admit trivial solutions that do not align with the notion of explainability. Instead, we argue that a modified GIB principle may be used to avoid the aforementioned trivial solutions. We further introduce a novel factorized explanation model with theoretical performance guarantees. The modified GIB is used to analyze the structural properties of the proposed factorized explainer. We conduct extensive experiments on both synthetic and real-world datasets to validate the effectiveness of our proposed factorized explainer.

Runtime Analysis of the (μ + 1) GA: Provable Speed-Ups from Strong Drift towards Diverse Populations

Most evolutionary algorithms used in practice heavily employ crossover. In contrast, the rigorous understanding of how crossover is beneficial is largely lagging behind. In this work, we make a considerable step forward by analyzing the population dynamics of the (µ+1) genetic algorithm when optimizing the Jump benchmark. We observe (and prove via mathematical means) that once the population contains two different individuals on the local optimum, the diversity in the population increases in expectation. From this drift towards more diverse states, we show that a diversity suitable for crossover to be effective is reached quickly and, more importantly, then persists for a time that is at least exponential in the population size µ. This drastically improves over the previously best known guarantee, which is only quadratic in µ. Our new understanding of the population dynamics easily gives stronger performance guarantees. In particular, we derive that population sizes logarithmic in the problem size n suffice to gain an Ω(n)-factor runtime improvement from crossover (previous works achieved comparable bounds only with µ = Θ(n) or a non-standard mutation rate).

Performance Guarantee for Autonomous Robotic Missions using Resource Management: The PANORAMA Approach

This paper proposes the PANORAMA approach, which is designed to dynamically and autonomously manage the allocation of a robot’s hardware and software resources during fully autonomous mission. This behavioral autonomy approach guarantees the satisfaction of the mission performance constraints. This article clarifies the concept of performance for autonomous robotic missions and details the different phases of the PANORAMA approach. Finally, it focuses on an experimental implementation on a patrolling mission example.

Learning Conservation Laws in Unknown Quantum Dynamics

We present a learning algorithm for discovering conservation laws given as sums of geometrically local observables in quantum dynamics. This includes conserved quantities that arise from local and global symmetries in closed and open quantum many-body systems. The algorithm combines the classical shadow formalism for estimating expectation values of observable and data analysis techniques based on singular value decompositions and robust polynomial interpolation to discover all such conservation laws in unknown quantum dynamics with rigorous performance guarantees. Our method can be directly realized in quantum experiments, which we illustrate with numerical simulations, using closed and open quantum system dynamics in a Z2 gauge theory and in many-body localized spin chains. Published by the American Physical Society 2024

Iterative learning robust optimization - with application to medium optimization of CHO cell cultivation in continuous monoclonal antibody production

In the presence of uncertainty, the optimum obtained based on a nominal identified model can neither provide any performance guarantee nor ensure that critical constraints are satisfied, which is crucial for e.g., bioprocess applications characterized by a high degree of complexity combined with costly experiments. Hence, uncertainty should be considered in the optimization and, furthermore, experiments designed to reduce the uncertainty most important for optimization. Herein, we propose a general framework that combines model-based robust optimization with optimal experiment design. The proposed framework can take advantage of prior knowledge in the form of a mechanistic model structure, and the importance of this is demonstrated by comparing it to more standard black-box models typically employed in learning. Through optimal experiment design, we repeatedly reduce the uncertainty most relevant for optimization so as to maximize the potential for improving the worst-case performance by balancing between exploration and exploitation. This makes the proposed method an efficient model-based robust optimization framework, especially in cases with limited experimental resources. The main part of the paper focuses on the case with modeling uncertainty that can be reduced with the availability of more experimental data. Towards the end of the paper, we consider extending the method to also include inherent uncertainty, such as input uncertainty and unmeasured disturbances. The effectiveness of the method is illustrated through a realistic simulation case study of medium optimization of Chinese hamster ovary cell cultivation in continuous monoclonal antibody production, where the metabolic network consists of 23 extracellular metabolites and 126 reactions.

Heuristic reoptimization of time‐extended multi‐robot task allocation problems

AbstractProviding high quality solutions is crucial when solving NP‐hard time‐extended multi‐robot task allocation (MRTA) problems. Reoptimization, that is, the concept of making use of a known solution to an optimization problem instance when the solution to a similar problem instance is sought, is a promising and rather new research field in this application domain. However, so far no approximative time‐extended MRTA solution approaches exist for which guarantees on the resulting solution's quality can be given. We investigate the reoptimization problems of inserting as well as deleting a task to/from a time‐extended MRTA problem instance. For both problems, we can give performance guarantees in the form of an upper bound of 2 on the resulting approximation ratio for all heuristics fulfilling a mild assumption. We furthermore introduce specific solution heuristics and prove that smaller and tight upper bounds on the approximation ratio can be given for these heuristics if only temporal unconstrained tasks and homogeneous groups of robots are considered. A conclusory evaluation of the reoptimization heuristic demonstrates a near‐to‐optimal performance in application.

Learning to Order for Inventory Systems with Lost Sales and Uncertain Supplies

We consider a stochastic lost-sales inventory control system with lead time L over a planning horizon T. Supply is uncertain, and it is a function of the order quantity (because of random yield/capacity, etc.). We aim to minimize the T-period cost, a problem that is known to be computationally intractable even under known distributions of demand and supply. In this paper, we assume that both the demand and supply distributions are unknown and develop a computationally efficient online learning algorithm. We show that our algorithm achieves a regret (i.e., the performance gap between the cost of our algorithm and that of an optimal policy over T periods) of [Formula: see text] when [Formula: see text]. We do so by (1) showing that our algorithm’s cost is higher by at most [Formula: see text] for any [Formula: see text] compared with an optimal constant-order policy under complete information (a widely used algorithm) and (2) leveraging the latter’s known performance guarantee from the existing literature. To the best of our knowledge, a finite sample [Formula: see text] (and polynomial in L) regret bound when benchmarked against an optimal policy is not known before in the online inventory control literature. A key challenge in this learning problem is that both demand and supply data can be censored; hence, only truncated values are observable. We circumvent this challenge by showing that the data generated under an order quantity q2 allow us to simulate the performance of not only q2 but also, q1 for all [Formula: see text], a key observation to obtain sufficient information even under data censoring. By establishing a high-probability coupling argument, we are able to evaluate and compare the performance of different order policies at their steady state within a finite time horizon. Because the problem lacks convexity, commonly used learning algorithms, such as stochastic gradient decent and bisection, cannot be applied, and instead, we develop an active elimination method that adaptively rules out suboptimal solutions. This paper was accepted by Victor Martínez-de-Albéniz, operations management. Funding: This work is supported by the National Science Foundation [Grant CCF-2312205]. Z. Zhou also acknowledges the New York University’s 2024 Center for Global Economy and Business [Faculty Research Grant] and New York University [Research Catalyst Prize]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.02476 .

Sample-Oriented Electricity Storage Sharing Mechanism Design With Performance Guarantees

Sample-Oriented Electricity Storage Sharing Mechanism Design With Performance Guarantees

Distribution Grid Line Outage Identification With Unknown Pattern and Performance Guarantee

Distribution Grid Line Outage Identification With Unknown Pattern and Performance Guarantee

Observer-Based Platoon Formation Control With Prescribed Performance Guarantees for Unmanned Surface Vehicles in Presence of Nonsmooth Input Characteristics

Observer-Based Platoon Formation Control With Prescribed Performance Guarantees for Unmanned Surface Vehicles in Presence of Nonsmooth Input Characteristics

Anticipated Wait and Its Effects on Consumer Choice, Pricing, and Assortment Management

Problem definition: We investigate the effects of waiting time, mainly due to production in a make-to-batch-order (MTBO) system, on consumer choice behavior, pricing, assortment, and model estimation. In an MTBO system, the seller/manufacturer first collects orders placed within a certain period of time into a batch and then starts the production process. After the production of all orders in a batch are complete, the products are then shipped and delivered to individual consumers. Because of batch production and shipping, the disutility of the waiting time exhibits negative externality. Methodology/results: We adopt the widely used multinomial logit (MNL) model as a starting point and incorporate the anticipated wait into consumers’ decision making. The derived model, referred to as the MNL with wait model, is a solution of the rational expectation equilibrium and is capable of capturing the effects of negative externality induced by anticipated wait that may change the substitution patterns dramatically. We characterize the multiproduct price optimization problem under the MNL with wait model by establishing a one-to-one mapping between the price vector and the choice probability vector. We find that firms tend to charge higher prices for time-consuming items and charge lower prices for time-saving items compared with the optimal prices under the standard MNL model. In addition to price competition, we also study the Cournot-type competition, in which the decision is the choice probability for each firm and establish the existence of a Nash equilibrium. For assortment optimization, we identify mild conditions under which the optimality of revenue-ordered assortments still holds. However, the assortment problem under the MNL with wait model is generally NP-hard, so we develop approximation algorithms with performance guarantees and provide an easy-to-compute tight upper bound. Moreover, we develop an efficient maximum likelihood-based algorithm for model calibration and further conduct numerical studies to showcase the importance of incorporating disutility due to wait in estimation, pricing, and assortment planning problems. Managerial implications: The MNL with wait model can increase prediction accuracy for consumers’ choice behavior especially when they are aware of the potential wait. Failure to take into account the effects of anticipated wait in firms’ decision making may lead to substantial losses. Funding: The research of C. Ke is supported in part by the National Natural Science Foundation of China [Grant 72101113]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2020.0346 .

Fast deterministic algorithms for non-submodular maximization with strong performance guarantees

Fast deterministic algorithms for non-submodular maximization with strong performance guarantees

Optimal Rate-Matrix Pruning For Heterogeneous Systems

We consider large-scale load balancing systems where processing time distribution of tasks depend on both task and server types. We analyze the system in the asymptotic regime where the number of task and server types tend to infinity proportionally to each other. In such heterogeneous setting, popular policies like Join Fastest Idle Queue (JFIQ), Join Fastest Shortest Queue (JFSQ) are known to perform poorly and they even shrink the stability region. Moreover, to the best of our knowledge, in this setup, finding a scalable policy with provable performance guarantee has been an open question prior to this work. In this paper, we propose and analyze two asymptotically delay-optimal dynamic load balancing approaches: (a) one that efficiently reserves the processing capacity of each server for "good" tasks and route tasks under the Join Idle Queue policy; and (b) a speed-priority policy that increases the probability of servers processing tasks at a high speed. Introducing a novel analytical framework and using the mean-field method and stochastic coupling arguments, we prove that both policies above achieve asymptotic zero queueing, whereby the probability that a typical task is assigned to an idle server tends to 1 as the system scales.