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We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.

In this paper, we study both multi-armed and contextual bandit problems in censored environments. Our goal is to estimate the performance loss due to censorship in the context of classical algorithms designed for uncensored environments. Our main contributions include the introduction of a broad class of censorship models and their analysis in terms of the effective dimension of the problem -- a natural measure of its underlying statistical complexity and main driver of the regret bound. In particular, the effective dimension allows us to maintain the structure of the original problem at first order, while embedding it in a bigger space, and thus naturally leads to results analogous to uncensored settings. Our analysis involves a continuous generalization of the Elliptical Potential Inequality, which we believe is of independent interest. We also discover an interesting property of decision-making under censorship: a transient phase during which initial misspecification of censorship is self-corrected at an extra cost, followed by a stationary phase that reflects the inherent slowdown of learning governed by the effective dimension. Our results are useful for applications of sequential decision-making models where the feedback received depends on strategic uncertainty (e.g., agents' willingness to follow a recommendation) and/or random uncertainty (e.g., loss or delay in arrival of information)., 45 pages, 5 figures, NeurIPS 2022

We study a market mechanism that sets edge prices to incentivize strategic agents to organize trips that efficiently share limited network capacity. This market allows agents to form groups to share trips, make decisions on departure times and route choices, and make payments to cover edge prices and other costs. We develop a new approach to analyze the existence and computation of market equilibrium, building on theories of combinatorial auctions and dynamic network flows. Our approach tackles the challenges in market equilibrium characterization arising from: (a) integer and network constraints on the dynamic flow of trips in sharing limited edge capacity; (b) heterogeneous and private preferences of strategic agents. We provide sufficient conditions on the network topology and agents' preferences that ensure the existence and polynomial-time computation of market equilibrium. We identify a particular market equilibrium that achieves maximum utilities for all agents, and is equivalent to the outcome of the classical Vickery Clark Grove mechanism. Finally, we extend our results to general networks with multiple populations and apply them to compute dynamic tolls for efficient carpooling in San Francisco Bay Area.

We study the problem of information provision by a strategic central planner who can publicly signal about an uncertain infectious risk parameter. Signalling leads to an updated public belief over the parameter, and agents then make equilibrium choices on whether to work remotely or in-person. The planner maintains a set of desirable outcomes for each realization of the uncertain parameter and seeks to maximize the probability that agents choose an acceptable outcome for the true parameter. We distinguish between stateless and stateful objectives. In the former, the set of desirable outcomes does not change as a function of the risk parameter, whereas in the latter it does. For stateless objectives, we reduce the problem to maximizing the probability of inducing mean beliefs that lie in intervals computable from the set of desirable outcomes. We derive the optimal signalling mechanism and show that it partitions the parameter domain into at most two intervals with the signals generated according to an interval-specific distribution. For the stateful case, we consider a practically relevant situation in which the planner can enforce in-person work capacity limits that progressively get more stringent as the risk parameter increases. We show that the optimal signalling mechanism for this case can be obtained by solving a linear program. We numerically verify the improvement in achieving desirable outcomes using our information design relative to no information and full information benchmarks.

This paper introduces a "green" routing game between multiple logistic operators (players), each owning a mixed fleet of internal combustion engine vehicle (ICEV) and electric vehicle (EV) trucks. Each player faces the cost of delayed delivery (due to charging requirements of EVs) and a pollution cost levied on the ICEVs. This cost structure models: 1) limited battery capacity of EVs and their charging requirement; 2) shared nature of charging facilities; 3) pollution cost levied by regulatory agency on the use of ICEVs. We characterize Nash equilibria of this game and derive a condition for its uniqueness. We also use the gradient projection method to compute this equilibrium in a distributed manner. Our equilibrium analysis is useful to analyze the trade-off faced by players in incurring higher delay due to congestion at charging locations when the share of EVs increases versus a higher pollution cost when the share of ICEVs increases. A numerical example suggests that to increase marginal pollution cost can dramatically reduce inefficiency of equilibria., 8 pages

A rapid transformation of current electric power and natural gas (NG) infrastructure is imperative to meet the mid-century goal of CO2 emissions reduction requires. This necessitates a long-term planning of the joint power-NG system under representative demand and supply patterns, operational constraints, and policy considerations. Our work is motivated by the computational and practical challenges associated with solving the generation and transmission expansion problem (GTEP) for joint planning of power-NG systems. Specifically, we focus on efficiently extracting a set of representative days from power and NG data in respective networks and using this set to reduce the computational burden required to solve the GTEP. We propose a Graph Autoencoder for Multiple time resolution Energy Systems (GAMES) to capture the spatio-temporal demand patterns in interdependent networks and account for differences in the temporal resolution of available data. The resulting embeddings are used in a clustering algorithm to select representative days. We evaluate the effectiveness of our approach in solving a GTEP formulation calibrated for the joint power-NG system in New England. This formulation accounts for the physical interdependencies between power and NG systems, including the joint emissions constraint. Our results show that the set of representative days obtained from GAMES not only allows us to tractably solve the GTEP formulation, but also achieves a lower cost of implementing the joint planning decisions.

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players' strategies and realized payoffs using Bayes's rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games, and enable us to characterize conditions under which learning leads to a complete information equilibrium., Comment: arXiv admin note: substantial text overlap with arXiv:2109.00719

Aerial images provide important situational awareness for responding to natural disasters such as hurricanes. They are well-suited for providing information for damage estimation and localization (DEL); i.e., characterizing the type and spatial extent of damage following a disaster. Despite recent advances in sensing and unmanned aerial systems technology, much of post-disaster aerial imagery is still taken by handheld DSLR cameras from small, manned, fixed-wing aircraft. However, these handheld cameras lack IMU information, and images are taken opportunistically post-event by operators. As such, DEL from such imagery is still a highly manual and time-consuming process. We propose an approach to both detect damage in aerial images and localize it in world coordinates, with specific focus on detecting and localizing flooding. The approach is based on using structure from motion to relate image coordinates to world coordinates via a projective transformation, using class activation mapping to detect the extent of damage in an image, and applying the projective transformation to localize damage in world coordinates. We evaluate the performance of our approach on post-event data from the 2016 Louisiana floods, and find that our approach achieves a precision of 88%. Given this high precision using limited data, we argue that this approach is currently viable for fast and effective DEL from handheld aerial imagery for disaster response., Version presented at NeurIPS 2021 AI+HADR workshop

This paper presents a modeling approach for probabilistic estimation of hurricane wind-induced damage to infrastructural assets. In our approach, we employ a Nonhomogeneous Poisson Process (NHPP) model for estimating spatially-varying probability distributions of damage as a function of hurricane wind field velocities. Specifically, we consider a physically-based, quadratic NHPP model for failures of overhead assets in electricity distribution systems. The wind field velocities are provided by Forecasts of Hurricanes using Large-Ensemble Outputs (FHLO), a framework for generating probabilistic hurricane forecasts. We use FHLO in conjunction with the NHPP model, such that the hurricane forecast uncertainties represented by FHLO are accounted for in estimating the probability distributions of damage. Furthermore, we evaluate the spatial variability and extent of hurricane damage under key wind field parameters (intensity, size, and asymmetries). By applying our approach to prediction of power outages (loss-of-service) in northwestern Florida due to Hurricane Michael (2018), we demonstrate a statistically significant relationship between outage rate and failure rate. Finally, we formulate parametric models that relate total damage and financial losses to the hurricane parameters of intensity and size. Overall, this paper's findings suggest that our approach is well-suited to jointly account for spatial variability and forecast uncertainty in the damage estimates, and is readily applicable to prediction of system loss-of-service due to the damage., Submitted to Risk Analysis, 21 pages (main text), 17 figures, includes appendix

In this paper, we address the existence and computation of competitive equilibrium in the transportation market for autonomous carpooling first proposed by [Ostrovsky and Schwarz, 2019]. At equilibrium, the market organizes carpooled trips over a transportation network in a socially optimal manner and sets the corresponding payments for individual riders and toll prices on edges. The market outcome ensures individual rationality, stability of carpooled trips, budget balance, and market clearing properties under heterogeneous rider preferences. We show that the question of market's existence can be resolved by proving the existence of an integer optimal solution of a linear programming problem. We characterize conditions on the network topology and riders' disutility for carpooling under which a market equilibrium can be computed in polynomial time. This characterization relies on ideas from the theory of combinatorial auctions and minimum cost network flow problem. Finally, we characterize a market equilibrium that achieves strategyproofness and maximizes welfare of individual riders.

We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In this dynamics, a belief estimate of the parameter is repeatedly updated given players' strategies and realized payoffs using Bayes's rule. Players adjust their strategies by accounting for best response strategies given the belief. We show that, with probability 1, beliefs and strategies converge to a fixed point, where the belief consistently estimates the payoff distribution for the strategy, and the strategy is an equilibrium corresponding to the belief. However, learning may not always identify the unknown parameter because the belief estimate relies on the game outcomes that are endogenously generated by players' strategies. We obtain sufficient and necessary conditions, under which learning leads to a globally stable fixed point that is a complete information Nash equilibrium. We also provide sufficient conditions that guarantee local stability of fixed point beliefs and strategies., Comment: arXiv admin note: text overlap with arXiv:2010.09128

Error-Correcting Output Codes (ECOCs) offer a principled approach for combining simple binary classifiers into multiclass classifiers. In this paper, we investigate the problem of designing optimal ECOCs to achieve both nominal and adversarial accuracy using Support Vector Machines (SVMs) and binary deep learning models. In contrast to previous literature, we present an Integer Programming (IP) formulation to design minimal codebooks with desirable error correcting properties. Our work leverages the advances in IP solvers to generate codebooks with optimality guarantees. To achieve tractability, we exploit the underlying graph-theoretic structure of the constraint set in our IP formulation. This enables us to use edge clique covers to substantially reduce the constraint set. Our codebooks achieve a high nominal accuracy relative to standard codebooks (e.g., one-vs-all, one-vs-one, and dense/sparse codes). We also estimate the adversarial accuracy of our ECOC-based classifiers in a white-box setting. Our IP-generated codebooks provide non-trivial robustness to adversarial perturbations even without any adversarial training.

We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players' strategies and realized payoffs using Bayes' rule. Players adjust their strategies by accounting for an equilibrium strategy or a best response strategy based on the updated belief. We prove that beliefs and strategies converge to a fixed point with probability 1. We also provide conditions that guarantee local and global stability of fixed points. Any fixed point belief consistently estimates the payoff distribution given the fixed point strategy profile. However, convergence to a complete information Nash equilibrium is not always guaranteed. We provide a sufficient and necessary condition under which fixed point belief recovers the unknown parameter. We also provide a sufficient condition for convergence to complete information equilibrium even when parameter learning is incomplete.

Traffic Management Centers (TMCs) routinely use traffic cameras to provide situational awareness regarding traffic, road, and weather conditions. Camera footage is quite useful for a variety of diagnostic purposes; yet, most footage is kept for only a few days, if at all. This is largely due to the fact that currently, identification of notable footage is done via manual review by human operators---a laborious and inefficient process. In this article, we propose a semantics-oriented approach to analyzing sequential image data, and demonstrate its application for automatic detection of real-world, anomalous events in weather and traffic conditions. Our approach constructs semantic vector representations of image contents from textual labels which can be easily obtained from off-the-shelf, pretrained image labeling software. These semantic label vectors are used to construct semantic topic signals---time series representations of physical processes---using the Latent Dirichlet Allocation (LDA) topic model. By detecting anomalies in the topic signals, we identify notable footage corresponding to winter storms and anomalous traffic congestion. In validation against real-world events, anomaly detection using semantic topic signals significantly outperforms detection using any individual label signal.

Electricity distribution networks (DNs) in many regions are increasingly subjected to disruptions caused by tropical storms. Distributed Energy Resources (DERs) can act as temporary supply sources to sustain "microgrids" resulting from disruptions. In this paper, we investigate the problem of suitable DER allocation to facilitate more efficient repair operations and faster recovery. First, we estimate the failure probabilities of DN components (lines) using a stochastic model of line failures which parametrically depends on the location-specific storm wind field. Next, we formulate a two-stage stochastic mixed integer program, which models the distribution utility's decision to allocate DERs in the DN (pre-storm stage); and accounts for multi-period decisions on optimal dispatch and line repair scheduling (post-storm stage). A key feature of this formulation is that it jointly optimizes electricity dispatch within the individual microgrids and the line repair schedules to minimize the sum of the cost of DER allocation and cost due to lost load. To illustrate our approach, we use the sample average approximation method to solve our problem for a small-size DN under different storm intensities and DER/crew constraints., Comment: 7 pages, 4 figures, accepted to 2018 IEEE SmartGridComm Conference

This article studies the value of information in route choice decisions when a fraction of players have access to high accuracy information about traffic incidents relative to others. To model such environments, we introduce a Bayesian congestion game, in which players have private information about incidents, and each player chooses her route on a network of parallel links. The links are prone to incidents that occur with an ex-ante known probability. The demand is comprised of two player populations: one with access to high accuracy incident information and another with low accuracy information, i.e. the populations differ only by their access to information. The common knowledge includes: (i) the demand and route cost functions, (ii) the fraction of highly-informed players, (iii) the incident probability, and (iv) the marginal type distributions induced by the information structure of the game. We present a full characterization of the Bayesian Wardrop Equilibrium of this game under the assumption that low information players receive no additional information beyond common knowledge. We also compute the cost to individual players and the social cost as a function of the fraction of highly-informed players when they receive perfectly accurate information. Our first result suggests that below a certain threshold of highly-informed players, both populations experience a reduction in individual cost, with the highly-informed players receiving a greater reduction. However, above this threshold, both populations realize the same equilibrium cost. Secondly, there exists another (lower or equal) threshold above which a further increase in the fraction of highly-informed players does not reduce the expected social costs. Thus, once a sufficiently large number of players are highly informed, wider distribution of more accurate information is ineffective at best, and otherwise socially harmful.

This article considers a two-player strategic game for network routing under link disruptions. Player 1 (defender) routes flow through a network to maximize her value of effective flow while facing transportation costs. Player 2 (attacker) simultaneously disrupts one or more links to maximize her value of lost flow but also faces cost of disrupting links. Linear programming duality in zero-sum games and the Max-Flow Min-Cut Theorem are applied to obtain properties that are satisfied in any Nash equilibrium. A characterization of the support of the equilibrium strategies is provided using graph-theoretic arguments. Finally, conditions under which these results extend to budget-constrained environments are also studied. These results extend the classical minimum cost maximum flow problem and the minimum cut problem to a class of security games on flow networks., Comment: The results in this paper only hold under a restrictive assumption on the class of networks (Assumption 1 in page 7). This makes the results inapplicable in practice, and further work is needed

Infrastructure systems are increasingly facing new security threats due to the vulnerabilities of cyber-physical components that support their operation. In this article, we investigate how the infrastructure operator (defender) should prioritize the investment in securing a set of facilities in order to reduce the impact of a strategic adversary (attacker) who can target a facility to increase the overall usage cost of the system. We adopt a game-theoretic approach to model the defender-attacker interaction and study two models: normal-form game -- where both players move simultaneously; and sequential game -- where attacker moves after observing the defender's strategy. For each model, we provide a complete characterization of how the set of facilities that are secured by the defender in equilibrium vary with the costs of attack and defense. Importantly, our analysis provides a sharp condition relating the cost parameters for which the defender has the first mover advantage. Specifically, we show that to fully deter the attacker from targeting any facility, the defender needs to proactively secure all "vulnerable facilities" at an appropriate level of effort. We illustrate the outcome of the attacker-defender interaction on a simple transportation network. We also suggest a dynamic learning setup to understand how this outcome can affect the ability of imperfectly informed users to make their decisions about using the system in the post-attack stage.

Mobile data traffic has been steadily rising in the past years. This has generated a significant interest in the deployment of incentive mechanisms to reduce peak-time congestion. Typically, the design of these mechanisms requires information about user demand and sensitivity to prices. Such information is naturally imperfect. In this paper, we propose a fixed-budget rebate mechanism that gives each user a reward proportional to his percentage contribution to the aggregate reduction in peak-time demand. For comparison, we also study a time-of-day pricing mechanism that gives each user a fixed reward per unit reduction of his peak-time demand. To evaluate the two mechanisms, we introduce a game-theoretic model that captures the public good nature of decongestion. For each mechanism, we demonstrate that the socially optimal level of decongestion is achievable for a specific choice of the mechanism's parameter. We then investigate how imperfect information about user demand affects the mechanisms' effectiveness. From our results, the fixed-budget rebate pricing is more robust when the users' sensitivity to congestion is “sufficiently” convex. This feature of the fixed-budget rebate mechanism is attractive for many situations of interest and is driven by its closed-loop property, i.e., the unit reward decreases as the peak-time demand decreases., National Science Foundation (U.S.) (Grant CNS-1239166), National Science Foundation (U.S.) (Grant CNS-0910711), National Science Foundation (U.S.) (CCF-0424422), United States. Air Force Office of Scientific Research (FA9550-06-1-0244)