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We consider a Stackelberg game in which a principal (she) establishes a two-stage contract with a non-myopic agent (he) whose type is unknown. The contract takes the form of an incentive function mapping the agent's first-stage action to his second-stage incentive. While the first-stage action reveals the agent's type under truthful play, a non-myopic agent could benefit from portraying a false type in the first stage to obtain a larger incentive in the second stage. The challenge is thus for the principal to design the incentive function so as to induce truthful play. We show that this is only possible with a constant, non-reactive incentive functions when the type space is continuous, whereas it can be achieved with reactive functions for discrete types. Additionally, we show that introducing an adjustment mechanism that penalizes inconsistent behavior across both stages allows the principal to design more flexible incentive functions.

This paper introduces WeatherFormer, a transformer encoder-based model designed to learn robust weather features from minimal observations. It addresses the challenge of modeling complex weather dynamics from small datasets, a bottleneck for many prediction tasks in agriculture, epidemiology, and climate science. WeatherFormer was pretrained on a large pretraining dataset comprised of 39 years of satellite measurements across the Americas. With a novel pretraining task and fine-tuning, WeatherFormer achieves state-of-the-art performance in county-level soybean yield prediction and influenza forecasting. Technical innovations include a unique spatiotemporal encoding that captures geographical, annual, and seasonal variations, adapting the transformer architecture to continuous weather data, and a pretraining strategy to learn representations that are robust to missing weather features. This paper for the first time demonstrates the effectiveness of pretraining large transformer encoder models for weather-dependent applications across multiple domains.

The problem of sample complexity of online reinforcement learning is often studied in the literature without taking into account any partial knowledge about the system dynamics that could potentially accelerate the learning process. In this paper, we study the sample complexity of online Q-learning methods when some prior knowledge about the dynamics is available or can be learned efficiently. We focus on systems that evolve according to an additive disturbance model of the form $S_{h+1} = f(S_h, A_h) + W_h$, where $f$ represents the underlying system dynamics, and $W_h$ are unknown disturbances independent of states and actions. In the setting of finite episodic Markov decision processes with $S$ states, $A$ actions, and episode length $H$, we present an optimistic Q-learning algorithm that achieves $\tilde{\mathcal{O}}(\text{Poly}(H)\sqrt{T})$ regret under perfect knowledge of $f$, where $T$ is the total number of interactions with the system. This is in contrast to the typical $\tilde{\mathcal{O}}(\text{Poly}(H)\sqrt{SAT})$ regret for existing Q-learning methods. Further, if only a noisy estimate $\hat{f}$ of $f$ is available, our method can learn an approximately optimal policy in a number of samples that is independent of the cardinalities of state and action spaces. The sub-optimality gap depends on the approximation error $\hat{f}-f$, as well as the Lipschitz constant of the corresponding optimal value function. Our approach does not require modeling of the transition probabilities and enjoys the same memory complexity as model-free methods., Comment: Published in the 38th Annual AAAI Conference on Artificial Intelligence

Eco-driving emerges as a cost-effective and efficient strategy to mitigate greenhouse gas emissions in urban transportation networks. Acknowledging the persuasive influence of incentives in shaping driver behavior, this paper presents the `eco-planner,' a digital platform devised to promote eco-driving practices in urban transportation. At the outset of their trips, users provide the platform with their trip details and travel time preferences, enabling the eco-planner to formulate personalized eco-driving recommendations and corresponding incentives, while adhering to its budgetary constraints. Upon trip completion, incentives are transferred to users who comply with the recommendations and effectively reduce their emissions. By comparing our proposed incentive mechanism with a baseline scheme that offers uniform incentives to all users, we demonstrate that our approach achieves superior emission reductions and increased user compliance with a smaller budget.

Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters. If there is shared structure among systems however, it may be possible to leverage data from other systems to help estimate individual parameters, which could otherwise be non-identifiable. In this paper, we assume systems share a latent low-dimensional parameter space and propose a method for recovering $d$-dimensional parameters for $N$ different linear systems, even when there are only $T

The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that one can learn the deterministic non-stationary components accurately using multivariate Singular Spectrum Analysis (mSSA) in the absence of a correlated stationary component; meanwhile, in the absence of deterministic non-stationary components, the Autoregressive (AR) stationary component can also be learnt readily, e.g. via Ordinary Least Squares (OLS). However, a theoretical underpinning of multi-stage learning algorithms involving both deterministic and stationary components has been absent in the literature despite its pervasiveness. We resolve this open question by establishing desirable theoretical guarantees for a natural two-stage algorithm, where mSSA is first applied to estimate the non-stationary components despite the presence of a correlated stationary AR component, which is subsequently learned from the residual time series. We provide a finite-sample forecasting consistency bound for the proposed algorithm, SAMoSSA, which is data-driven and thus requires minimal parameter tuning. To establish theoretical guarantees, we overcome three hurdles: (i) we characterize the spectra of Page matrices of stable AR processes, thus extending the analysis of mSSA; (ii) we extend the analysis of AR process identification in the presence of arbitrary bounded perturbations; (iii) we characterize the out-of-sample or forecasting error, as opposed to solely considering model identification. Through representative empirical studies, we validate the superior performance of SAMoSSA compared to existing baselines. Notably, SAMoSSA's ability to account for AR noise structure yields improvements ranging from 5% to 37% across various benchmark datasets.

We consider games of incomplete information in which the players' payoffs depend both on a privately observed type and an unknown but common "state of nature". External to the game, a data provider knows the state of nature and sells information to the players, thus solving a joint information and mechanism design problem: deciding which information to sell while eliciting the player' types and collecting payments. We restrict ourselves to a general class of symmetric games with quadratic payoffs that includes games of both strategic substitutes (e.g. Cournot competition) and strategic complements (e.g. Bertrand competition, Keynesian beauty contest). By to the Revelation Principle, the sellers' problem reduces to designing a mechanism that truthfully elicits the player' types and sends action recommendations that constitute a Bayes Correlated Equilibrium of the game. We fully characterize the class of all such Gaussian mechanisms (where the joint distribution of actions and private signals is a multivariate normal distribution) as well as the welfare- and revenue- optimal mechanisms within this class. For games of strategic complements, the optimal mechanisms maximally correlate the players' actions, and conversely maximally anticorrelate them for games of strategic substitutes. In both cases, for sufficiently large uncertainty over the players' types, the recommendations are deterministic (and linear) conditional on the state and the type reports, but they are not fully revealing.

In addition to its public health crisis, COVID-19 pandemic has led to the shutdown and closure of workplaces with an estimated total cost of more than $16 trillion. Given the long hours an average person spends in buildings and indoor environments, this research article proposes data-driven control strategies to design optimal indoor airflow to minimize the exposure of occupants to viral pathogens in built environments. A general control framework is put forward for designing an optimal velocity field and proximal policy optimization, a reinforcement learning algorithm is employed to solve the control problem in a data-driven fashion. The same framework is used for optimal placement of disinfectants to neutralize the viral pathogens as an alternative to the airflow design when the latter is practically infeasible or hard to implement. We show, via simulation experiments, that the control agent learns the optimal policy in both scenarios within a reasonable time. The proposed data-driven control framework in this study will have significant societal and economic benefits by setting the foundation for an improved methodology in designing case-specific infection control guidelines that can be realized by affordable ventilation devices and disinfectants.

Demand response involves system operators using incentives to modulate electricity consumption during peak hours or when faced with an incidental supply shortage. However, system operators typically have imperfect information about their customers' baselines, that is, their consumption had the incentive been absent. The standard approach to estimate the reduction in a customer's electricity consumption then is to estimate their counterfactual baseline. However, this approach is not robust to estimation errors or strategic exploitation by the customers and can potentially lead to overpayments to customers who do not reduce their consumption and underpayments to those who do. Moreover, optimal power consumption reductions of the customers depend on the costs that they incur for curtailing consumption, which in general are private knowledge of the customers, and which they could strategically misreport in an effort to improve their own utilities even if it deteriorates the overall system cost. The two-stage mechanism proposed in this paper circumvents the aforementioned issues. In the day-ahead market, the participating loads are required to submit only a probabilistic description of their next-day consumption and costs to the system operator for day-ahead planning. It is only in real-time, if and when called upon for demand response, that the loads are required to report their baselines and costs. They receive credits for reductions below their reported baselines. The mechanism for calculating the credits guarantees incentive compatibility of truthful reporting of the probability distribution in the day-ahead market and truthful reporting of the baseline and cost in real-time. The mechanism can be viewed as an extension of the celebrated Vickrey-Clarke-Groves mechanism augmented with a carefully crafted second-stage penalty for deviations from the day-ahead bids.

We address the problem of mechanism design for two-stage repeated stochastic games -- a novel setting using which many emerging problems in next-generation electricity markets can be readily modeled. Repeated playing affords the players a large class of strategies that adapt a player's actions to all past observations and inferences obtained therefrom. In other settings such as iterative auctions or dynamic games where a large strategy space of this sort manifests, it typically has an important implication for mechanism design: It may be impossible to obtain truth-telling as a dominant strategy equilibrium. Consequently, in such scenarios, it is common to settle for mechanisms that render truth-telling only a Nash equilibrium, or variants thereof, even though Nash equilibria are known to be poor models of real-world behavior. This is owing to each player having to make overly specific assumptions about the behaviors of the other players to employ their Nash equilibrium strategy, which they may not make. In general, the lesser the burden of speculation in an equilibrium, the more plausible it is that it models real-world behavior. Guided by this maxim, we introduce a new notion of equilibrium called Dominant Strategy Non-Bankrupting Equilibrium (DNBE) which requires the players to make very little assumptions about the behavior of the other players to employ their equilibrium strategy. Consequently, a mechanism that renders truth-telling a DNBE as opposed to only a Nash equilibrium could be quite effective in molding real-world behavior along truthful lines. We present a mechanism for two-stage repeated stochastic games that renders truth-telling a Dominant Strategy Non-Bankrupting Equilibrium. The mechanism also guarantees individual rationality and maximizes social welfare. Finally, we describe an application of the mechanism to design demand response markets.

Data buyers compete in a game of incomplete information about which a single data seller owns some payoff-relevant information. The seller faces a joint information- and mechanism-design problem: deciding which information to sell, while eliciting the buyers' types and imposing payments. We derive the welfare- and revenue-optimal mechanisms for a class of games with binary actions and states. Our results highlight the critical properties of selling information in competitive environments: (i) the negative externalities arising from buyer competition increase the profitability of recommending the correct action to one buyer exclusively; (ii) for the buyers to follow the seller's recommendations, the degree of exclusivity must be limited; (iii) the buyers' obedience constraints also limit the distortions in the allocation of information introduced by a monopolist seller; (iv) as competition becomes fiercer, these limitations become more severe, weakening the impact of market power on the allocation of information.

Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are "missing completely at random" (MCAR), i.e., each entry is revealed at random, independent of everything else, with uniform probability. This is likely unrealistic due to the presence of "latent confounders", i.e., unobserved factors that determine both the entries of the underlying matrix and the missingness pattern in the observed matrix. For example, in the context of movie recommender systems -- a canonical application for matrix completion -- a user who vehemently dislikes horror films is unlikely to ever watch horror films. In general, these confounders yield "missing not at random" (MNAR) data, which can severely impact any inference procedure that does not correct for this bias. We develop a formal causal model for matrix completion through the language of potential outcomes, and provide novel identification arguments for a variety of causal estimands of interest. We design a procedure, which we call "synthetic nearest neighbors" (SNN), to estimate these causal estimands. We prove finite-sample consistency and asymptotic normality of our estimator. Our analysis also leads to new theoretical results for the matrix completion literature. In particular, we establish entry-wise, i.e., max-norm, finite-sample consistency and asymptotic normality results for matrix completion with MNAR data. As a special case, this also provides entry-wise bounds for matrix completion with MCAR data. Across simulated and real data, we demonstrate the efficacy of our proposed estimator.

Access to capital is a major constraint for economic growth in the developing world. Yet those attempting to lend in this space face high defaults due to their inability to distinguish creditworthy borrowers from the rest. In this paper, we propose two novel scoring mechanisms that incentivize community members to truthfully report their signal on the creditworthiness of others in their community. We first design a truncated asymmetric scoring-rule for a setting where the lender has no liquidity constraints. We then derive a novel, strictly-proper VCG scoring mechanism for the liquidity-constrained setting. Whereas Chen et al. [2011] give an impossibility result for an analogous setting in which sequential reports are made in the context of decision markets, we achieve a positive result through appeal to interim beliefs about the reports of others in a setting with simultaneous reports.Moreover, the use of VCG methods allows for the integration of linear belief aggregation methods., Comment: 17 pages, submitted to WINE

Most of the new technological changes in power systems are expected to take place in distribution grids. The enormous potential for distribution flexibility could meet the transmission system's needs, changing the paradigm of generator-centric energy and ancillary services provided to a demand-centric one, by placing more importance on smaller resources, such as flexible demands and electric vehicles. For unlocking such capabilities, it is essential to understand the aggregated flexibility that can be harvested from the large population of new technologies located in distribution grids. Distribution grids, therefore, could provide aggregated flexibility at the transmission level. To date, most computational methods for estimating the aggregated flexibility at the interface between distribution grids and transmission grids have the drawback of requiring significant computational time, which hinders their applicability. This paper presents a new algorithm, coined as QuickFlex} for constructing the flexibility domain of distribution grids. Contrary to previous methods, a priory flexibility domain accuracy can be selected. Our method requires few iterations for constructing the flexibility region. The number of iterations needed is mainly independent of the distribution grid's input size and flexible elements. Numerical experiments are performed in four grids ranging from 5 nodes to 123 nodes. It is shown that QuickFlex outperforms existing proposals in the literature in both speed and accuracy.

The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning method to identify meaningful low-dimensional state and action representations from empirical trajectories. The method exploits the MDP's tensor structure by kernelization, importance sampling and low-Tucker-rank approximation. This method can be further used to cluster states and actions respectively and find the best discrete MDP abstraction. We provide sharp statistical error bounds for tensor concentration and the preservation of diffusion distance after embedding. We further prove that the learned state/action abstractions provide accurate approximations to latent block structures if they exist, enabling function approximation in downstream tasks such as policy evaluation.

In this work, inspired by secret sharing schemes, we introduce a privacy-preserving approach for network consensus, by which all nodes in a network can reach an agreement on their states without exposing the individual state to neighbors. With the privacy degree defined for the agents, the proposed method makes the network resistant to the collusion of any given number of neighbors, and protects the consensus procedure from communication eavesdropping. Unlike existing works, the proposed privacy-preserving algorithm is resilient to node failures. When a node fails, the method offers the possibility of rebuilding the lost node via the information kept in its neighbors, even though none of the neighbors knows the exact state of the failing node. Moreover, it is shown that the proposed method can achieve consensus and average consensus almost surely, when the agents have arbitrary privacy degrees and a common privacy degree, respectively. To illustrate the theory, two numerical examples are presented., Comment: 14 pages, 5 figures

We study the problem of nonstochastic bandits with expert advice, extending the setting from finitely many experts to any countably infinite set: A learner aims to maximize the total reward by taking actions sequentially based on bandit feedback while benchmarking against a set of experts. We propose a variant of Exp4.P that, for finitely many experts, enables inference of correct expert rankings while preserving the order of the regret upper bound. We then incorporate the variant into a meta-algorithm that works on infinitely many experts. We prove a high-probability upper bound of $\tilde{\mathcal{O}} \big( i^*K + \sqrt{KT} \big)$ on the regret, up to polylog factors, where $i^*$ is the unknown position of the best expert, $K$ is the number of actions, and $T$ is the time horizon. We also provide an example of structured experts and discuss how to expedite learning in such case. Our meta-learning algorithm achieves optimal regret up to polylog factors when $i^* = \tilde{\mathcal{O}} \big( \sqrt{T/K} \big)$. If a prior distribution is assumed to exist for $i^*$, the probability of optimality increases with $T$, the rate of which can be fast., Comment: Added numerical experiments

A key obstacle to increasing renewable energy penetration in the power grid is the lack of utility-scale storage capacity. Transportation electrification has the potential to overcome this obstacle since Electric Vehicles (EVs) that are not in transit can provide battery storage as a service to the grid. This is referred to as EV-Power grid integration, and could potentially be a key milestone in the pathway to decarbonize the electricity and the transportation sectors. We first show that if EV-Power grid integration is not done carefully, then contrary to improving the cost efficiency of operating the grid, it could in fact be counterproductive to it. This fundamentally occurs due to two phenomena operating in tandem - the randomness of EV usage patterns and the possibility of strategic behavior by EV operators. We present a market-based solution to address this issue. Specifically, we develop a mechanism for energy storage markets using which the system operator can efficiently integrate a fleet of strategic EVs with random usage patterns into the grid, utilize them for storage, and satisfy the demand at minimum possible cost.

The COVID-19 pandemic began over two years ago, yet schools, businesses, and other organizations are still struggling to keep the risk of disease outbreak low while returning to (near) normal functionality. Observations from these past years suggest that this goal can be achieved through the right balance of mitigation strategies, which may include some combination of mask use, vaccinations, viral testing, and contact tracing. The choice of mitigation measures will be uniquely based on the needs and available resources of each organization. This article presents practical guidance for creating these policies based on an analytical model of disease spread that captures the combined effects of each of these interventions. The resulting guidance is tested through simulation across a wide range of parameters and used to discuss the spread of disease on college campuses.

This paper proposes a privacy-preserving algorithm to solve the average consensus problem based on Shamir's secret sharing scheme, in which a network of agents reach an agreement on their states without exposing their individual state until an agreement is reached. Unlike other methods, the proposed algorithm renders the network resistant to the collusion of any given number of neighbors (even with all neighbors' colluding). Another virtue of this work is that such a method can protect the network consensus procedure from eavesdropping.

The novel coronavirus disease (COVID-19) has rapidly spread around the globe in 2020, with the U.S. becoming the epicenter of COVID-19 cases since late March. As the U.S. begins to gradually resume economic activity, it is imperative for policymakers and power system operators to take a scientific approach to understanding and predicting the impact on the electricity sector. Here, we release a first-of-its-kind cross-domain open-access data hub, integrating data from across all existing U.S. wholesale electricity markets with COVID-19 case, weather, cellular location, and satellite imaging data. Leveraging cross-domain insights from public health and mobility data, we uncover a significant reduction in electricity consumption across that is strongly correlated with the rise in the number of COVID-19 cases, degree of social distancing, and level of commercial activity., Comment: This paper has been accepted for publication by Joule. The manuscript can also be accessed from EnerarXiv: http://www.enerarxiv.org/page/thesis.html?id=1989

The design of data markets has gained importance as firms increasingly use machine learning models fueled by externally acquired training data. A key consideration is the externalities firms face when data, though inherently freely replicable, is allocated to competing firms. In this setting, we demonstrate that a data seller's optimal revenue increases as firms can pay to prevent allocations to others. To do so, we first reduce the combinatorial problem of allocating and pricing multiple datasets to the auction of a single digital good by modeling utility for data through the increase in prediction accuracy it provides. We then derive welfare and revenue maximizing mechanisms, highlighting how the form of firms' private information - whether the externalities one exerts on others is known, or vice-versa - affects the resulting structures. In all cases, under appropriate assumptions, the optimal allocation rule is a single threshold per firm, where either all data is allocated or none is., Comment: Corrected error in previously labeled Theorem 3

Smart buildings have great potential for shaping an energy-efficient, sustainable, and more economic future for our planet as buildings account for approximately 40% of the global energy consumption. Future of the smart buildings lies in using sensory data for adaptive decision making and control that is currently gloomed by the key challenge of learning a good control policy in a short period of time in an online and continuing fashion. To tackle this challenge, an event-triggered -- as opposed to classic time-triggered -- paradigm, is proposed in which learning and control decisions are made when events occur and enough information is collected. Events are characterized by certain design conditions and they occur when the conditions are met, for instance, when a certain state threshold is reached. By systematically adjusting the time of learning and control decisions, the proposed framework can potentially reduce the variance in learning, and consequently, improve the control process. We formulate the micro-climate control problem based on semi-Markov decision processes that allow for variable-time state transitions and decision making. Using extended policy gradient theorems and temporal difference methods in a reinforcement learning set-up, we propose two learning algorithms for event-triggered control of micro-climate in buildings. We show the efficacy of our proposed approach via designing a smart learning thermostat that simultaneously optimizes energy consumption and occupants' comfort in a test building.

We propose a means to relate properties of an interconnected system to its separate component systems in the presence of cascade-like phenomena. Building on a theory of interconnection reminiscent of the behavioral approach to systems theory, we introduce the notion of generativity, and its byproduct, generative effects. Cascade effects, enclosing contagion phenomena and cascading failures, are seen as instances of generative effects. The latter are precisely the instances where properties of interest are not preserved or behave very badly when systems interact. The goal is to overcome that obstruction. We will show how to extract mathematical objects from the systems, that encode their generativity: their potential to generate new phenomena upon interaction. Those objects may then be used to link the properties of the interconnected system to its separate systems. Such a link will be executed through the use of exact sequences from commutative algebra., Comment: 31 pages

We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than thinking of a system as a pair $(\mathbb{U}, \mathcal{B})$, we begin by thinking of it as an injective map from $\mathcal{B} \rightarrow \mathbb{U}$. This relative perspective naturally brings about the sought structure, which we summarize in three points. First, the separation of behavioral equations and behavior is developed through two spaces, one of syntax and another of semantics, linked by an interpretation map. Second, the notion of interconnection and variable sharing is shown to be a construction of the same nature as that of gluing topological spaces or taking amalgamated sums of algebraic objects. Third, the notion of interconnection instantiates to both the syntax space and the semantics space, and the interpretation map is shown to preserve the interconnection when going from syntax to semantics. This pattern, in its generality, is made precise by borrowing very basic constructs from the language of categories and functors., Comment: 25 pages

We argue that the mathematical structure, enabling certain cascading and emergent phenomena to intuitively emerge, coincides with Galois connections. We introduce the notion of generative effects to formally capture such phenomena. We establish that these effects arise, via a notion of a veil, from either concealing mechanisms in a system or forgetting characteristics from it. The goal of the work is to initiate a mathematical base that enables us to further study such phenomena. In particular, generative effects can be further linked to a certain loss of exactness. Homological algebra, and related algebraic methods, may then be used to characterize the effects., Comment: 37 pages

We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss the effect of physical constraints on robustness to loss in link capacities. In the dynamical setting, we review several settings in which small gain type analysis provides tight robustness guarantees for linear dynamics over finite networks towards worst-case and stochastic disturbances. We also discuss network flow dynamic settings where nonlinear techniques facilitate in understanding the effect on robustness of constraints on capacity and information, substituting information with control action, and cascading failure. We also contrast the latter with a representative contagion model. For asymptotically large networks, we discuss the role of network properties in connecting microscopic shocks to emergent macroscopic fluctuations under linear dynamics as well as for economic networks at equilibrium. Through the review of these results, the paper aims to achieve two objectives. First, to highlight selected settings in which the role of interconnectivity structure of a network on its robustness is well-understood. Second, to highlight a few additional settings in which existing system theoretic tools give tight robustness guarantees, and which are also appropriate avenues for future network-theoretic investigations., Comment: To appear in Annual Review of Control, Robotics, and Autonomous Systems

We address the problem of learning the parameters of a mean square stable switched linear systems (SLS) with unknown latent space dimension, or \textit{order}, from its noisy input--output data. In particular, we focus on learning a good lower order approximation of the underlying model allowed by finite data. Motivated by subspace-based algorithms in system theory, we construct a Hankel-like matrix from finite noisy data using ordinary least squares. Such a formulation circumvents the non-convexities that arise in system identification, and allows for accurate estimation of the underlying SLS as data size increases. Since the model order is unknown, the key idea of our approach is model order selection based on purely data dependent quantities. We construct Hankel-like matrices from data of dimension obtained from the order selection procedure. By exploiting tools from theory of model reduction for SLS, we obtain suitable approximations via singular value decomposition (SVD) and show that the system parameter estimates are close to a balanced truncated realization of the underlying system with high probability., Comment: 22 pages, 2 figures, to be submitted to IEEE TAC. Shorter version appeared in CDC 2019 as Nonparametric System identification of Stochastic Switched Linear Systems

Personal data is essential in showing users targeted ads - the economic backbone of the web. Still, there are major inefficiencies in how data is transacted online: (1) users don't decide what information is released nor get paid for this privacy loss; (2) algorithmic advertisers are stuck in inefficient long-term contracts where they purchase user data without knowing the value it provides. This paper proposes a system, Zorro, which aims to rectify aforementioned two problems. As the main contribution, we provide a natural, 'absolute' definition of 'Value of Data' (VoD) - for any quantity of interest, it is the delta between an individual's value and population mean. The challenge remains how to operationalize this definition, independently of a buyer's model for VoD. We propose a model-agnostic solution, relying on matrix estimation, and use it to estimate click-through-rate (CTR), as an example. Regarding (2), Zorro empowers advertisers to measure value of user data on a query-by-query basis and based only on the increase in accuracy it provides in estimating CTR. In contrast advertisers currently engage in inefficient long-term data contracts with third party data sellers. We highlight two results on a large ad-click dataset: (i) our system has R^2=0.58, in line with best-in-class results for related problems (e.g. content recommendation). Crucially, our system is model-agnostic - we estimate CTR without accessing an advertiser's proprietary models, a required property of any such pricing system;(ii) our experiments show selling user data has incremental value ranging from 30%-69% depending on ad category. Roughly, this translates to at least USD 16 Billion loss in value for advertisers if user data is not provided. Regarding (1), in addition to allowing users to get paid for data sharing, we extend our mathematical framework to when users provide explicit intent.

We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus on learning the best lower order approximation allowed by finite data. Motivated by subspace algorithms in systems theory, where the doubly infinite system Hankel matrix captures both order and good lower order approximations, we construct a Hankel-like matrix from noisy finite data using ordinary least squares. This circumvents the non-convexities that arise in system identification, and allows accurate estimation of the underlying LTI system. Our results rely on careful analysis of self-normalized martingale difference terms that helps bound identification error up to logarithmic factors of the lower bound. We provide a data-dependent scheme for order selection and find an accurate realization of system parameters, corresponding to that order, by an approach that is closely related to the Ho-Kalman subspace algorithm. We demonstrate that the proposed model order selection procedure is not overly conservative, i.e., for the given data length it is not possible to estimate higher order models or find higher order approximations with reasonable accuracy., Comment: Restructuring the paper

Spurred by the growth of transportation network companies and increasing data capabilities, vehicle routing and ride-matching algorithms can improve the efficiency of private transportation services. However, existing routing solutions do not address where drivers should travel after dropping off a passenger and before receiving the next passenger ride request, i.e., during the between-ride period. We address this problem by developing an efficient algorithm to find the optimal policy for drivers between rides in order to maximize driver profits. We model the road network as a graph, and we show that the between-ride routing problem is equivalent to a stochastic shortest path problem, an infinite dynamic program with no discounting. We prove under reasonable assumptions that an optimal routing policy exists that avoids cycles; policies of this type can be efficiently found. We present an iterative approach to find an optimal routing policy. Our approach can account for various factors, including the frequency of passenger ride requests at different locations, traffic conditions, and surge pricing. We demonstrate the effectiveness of the approach by implementing it on road network data from Boston and New York City., Comment: 8 pages

This paper addresses two fundamental problems in the context of jump linear systems (JLS). The first problem is concerned with characterizing the minimal state space dimension solely from input-output pairs and without any knowledge of the number of mode switches. The second problem is concerned with characterizing the number of discrete modes of the JLS. For the first problem, we develop a linear system theory based approach and construct an appropriate Hankel-like matrix. The rank of this matrix gives us the state space dimension. For the second problem we show that minimal number of modes corresponds to the minimal rank of a positive semi-definite matrix obtained via a non--convex formulation., Comment: 8 pages, Accepted to Conference on Decision and Control (CDC) 2018: Errata to conference version - changes to Algorithm 1 and Theorem 1

In this work, we aim to design a data marketplace; a robust real-time matching mechanism to efficiently buy and sell training data for Machine Learning tasks. While the monetization of data and pre-trained models is an essential focus of industry today, there does not exist a market mechanism to price training data and match buyers to sellers while still addressing the associated (computational and other) complexity. The challenge in creating such a market stems from the very nature of data as an asset: (i) it is freely replicable; (ii) its value is inherently combinatorial due to correlation with signal in other data; (iii) prediction tasks and the value of accuracy vary widely; (iv) usefulness of training data is difficult to verify a priori without first applying it to a prediction task. As our main contributions we: (i) propose a mathematical model for a two-sided data market and formally define the key associated challenges; (ii) construct algorithms for such a market to function and analyze how they meet the challenges defined. We highlight two technical contributions: (i) a new notion of 'fairness' required for cooperative games with freely replicable goods; (ii) a truthful, zero regret mechanism to auction a class of combinatorial goods based on utilizing Myerson's payment function and the Multiplicative Weights algorithm. These might be of independent interest.

We consider the problem of robustness in large consensus networks that occur in many areas such as distributed optimization. Robustness, in this context, is the scaling of performance measures, e.g. H2-norm, as a function of network dimension. We provide a formal framework to quantify the relation between such performance scaling and the convergence speed of the network. Specifically, we provide upper and lower bounds for the convergence speed in terms of robustness and discuss how these bounds scale with the network topology. The main contribution of this work is that we obtain tight bounds, that hold regardless of network topology. The work here also encompasses some results in convergence time analysis in previous literature., Comment: 7 pages, 3 figures, IEEE American Control Conference 2018 (Accepted; To be published)

This paper examines the dependence of network performance measures on network size and considers scaling results for large networks. We connect two performance measures that are well studied, but appear to be unrelated. The first measure is concerned with energy metrics, namely the $\Hcal_2$--norm of a network, which arises in control theory applications. The second measure is concerned with the notion of "tail risk" which arises in economic and financial networks. We study the question of why such performance measures may deteriorate at a faster rate than the growth rate of the network. We first focus on the energy metric and its well known connection to controllability Gramian of the underlying dynamical system. We show that undirected networks exhibit the most graceful energy growth rates as network size grows. This rate is quantified completely by the proximity of spectral radius to unity or distance to instability. In contrast, we show that the simple characterization of energy in terms of network spectrum does not exist for directed networks. We demonstrate that, for any fixed distance to instability, energy of a directed network can grow at an exponentially faster rate. We provide general methods for manipulating networks to reduce energy. In particular, we prove that certain operations that increase the symmetry in a network cannot increase energy (in an order sense). Secondly, we focus on tail risk in economic and financial networks. In contrast to $\Hcal_2$--norm which arises from computing the expectation of energy in the network, tail risk focuses on tail probability behavior of network variables. Although the two measures differ substantially we show that they are precisely connected through the system Gramian. This surprising result explains why topology considerations rather than specific performance measures dictate the large scale behavior of networks., Comment: 15 pages, 11 figures, submitted to IEEE Transactions on Control of Network Systems (under review after major revision)

In coalitional games, traditional coalitional game theory does not apply if different participants hold different opinions about the payoff function that corresponds to each subset of the coalition. In this paper, we propose a framework in which players can exchange opinions about their views of payoff functions and then decide the distribution of the value of the grand coalition. When all players are truth-telling, the problem of opinion consensus is decoupled from the coalitional game, but interesting dynamics will arise when players are strategic in the consensus phase. Assuming that all players are rational, the model implies that, if influential players are risk-averse, an efficient fusion of the distributed data is achieved at pure strategy Nash equilibrium, meaning that the average opinion will not drift. Also, without the assumption that all players are rational, each player can use an algorithmic R-learning process, which gives the same result as the pure strategy Nash equilibrium with rational players., Comment: Accepted by IEEE Conference on Decision and Control 2017

This paper analyzes the impact of peer effects on electricity consumption of a network of rational, utility-maximizing users. Users derive utility from consuming electricity as well as consuming less energy than their neighbors. However, a disutility is incurred for consuming more than their neighbors. To maximize the profit of the load-serving entity that provides electricity to such users, we develop a two-stage game-theoretic model, where the entity sets the prices in the first stage. In the second stage, consumers decide on their demand in response to the observed price set in the first stage so as to maximize their utility. To this end, we derive theoretical statements under which such peer effects reduce aggregate user consumption. Further, we obtain expressions for the resulting electricity consumption and profit of the load serving entity for the case of perfect price discrimination and a single price under complete information, and approximations under incomplete information. Simulations suggest that exposing only a selected subset of all users to peer effects maximizes the entity's profit., Comment: 9 pages, 4 figures

Load-serving entities which procure electricity from the wholesale electricity market to service end-users face significant quantity and price risks due to the volatile nature of electricity demand and quasi-fixed residential tariffs at which electricity is sold. This paper investigates strategies for load serving entities to hedge against such price risks. Specifically, we compute profit-maximizing portfolios of forward contract and call options as a function of the uncertain aggregate user demand. We compare the profit to the case of Demand Response, where users are offered monetary incentives to temporarily reduce their consumption during periods of supply shortages. Using smart meter data of residential customers in California, we simulate optimal portfolios and derive conditions under which Demand Response outperforms call options and forward contracts., Comment: 8 pages, 7 figures

Residential Demand Response has emerged as a viable tool to alleviate supply and demand imbalances of electricity, particularly during times when the electric grid is strained due a shortage of supply. Demand Response providers bid reduction capacity into the wholesale electricity market by asking their customers under contract to temporarily reduce their consumption in exchange for a monetary incentive. To contribute to the analysis of consumer behavior in response to such incentives, this paper formulates Demand Response as a Mechanism Design problem, where a Demand Response Provider elicits private information of its rational, profit-maximizing customers who derive positive expected utility by participating in reduction events. By designing an incentive compatible and individually rational mechanism to collect users' price elasticities of demand, the Demand Response provider can target the most susceptible users to incentives. We measure reductions by comparing the materialized consumption to the projected consumption, which we model as the "10-in-10"-baseline, the regulatory standard set by the California Independent System Operator. Due to the suboptimal performance of this baseline, we show, using consumption data of residential customers in California, that Demand Response Providers receive payments for "virtual reductions", which exist due to the inaccuracies of the baseline rather than actual reductions. Improving the accuracy of the baseline diminishes the contribution of these virtual reductions., Comment: 8 pages, 7 figures

We investigate the ability of a homogeneous collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. We derive explicit bounds on the battery capacity that can be offered, and show that there is a fundamental trade-off between the abilities of collective load to absorb and release energy at high aggregate rates. Finally, we introduce a new class of dynamic priority-driven feedback policies that balance these abilities, and characterize the batteries that they can emulate., Comment: arXiv admin note: substantial text overlap with arXiv:1610.01973

We investigate the ability of a homogeneous collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. We derive bounds on the battery capacity that can be realized and show that there are fundamental trade-offs between battery parameters. By characterizing the state trajectories under scheduling policies that emulate two illustrative batteries, we show that the trade-offs occur because the states that allow the loads to absorb and release energy at high aggregate rates are conflicting.

In this paper, we investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current particle densities. The density on each link has first order dynamics driven by the difference of its incoming and outgoing flows. A link irreversibly fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities do not necessarily help in preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. Our main result shows that systemic failures under feasible external inflows can always be averted through a proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it is much easier in practice to adjust the speed limits than to build more physical capacity or to alter routing decisions that are determined by social behavior.

This paper analyzes stability conditions for wholesale electricity markets under real-time retail pricing and realistic consumption models with memory, which explicitly take into account previous electricity prices and consumption levels. By passing on the current retail price of electricity from supplier to consumer and feeding the observed consumption back to the supplier, a closed-loop dynamical system for electricity prices and consumption arises whose stability is to be investigated. Under mild assumptions on the generation cost of electricity and consumers' backlog disutility functions, we show that, for consumer models with price memory only, market stability is achieved if the ratio between the consumers' marginal backlog disutility and the suppliers' marginal cost of supply remains below a fixed threshold. Further, consumer models with price and consumption memory can result in greater stability regions and faster convergence to the equilibrium compared to models with price memory alone, if consumption deviations from nominal demand are adequately penalized., Comment: 8 pages, 7 Figures, accepted to the 2017 American Control Conference

In this paper, we are concerned with the resilience of locally routed network flows with finite link capacities. In this setting, an external inflow is injected to the so-called origin nodes. The total inflow arriving at each node is routed locally such that none of the outgoing links are overloaded unless the node receives an inflow greater than its total outgoing capacity. A link irreversibly fails if it is overloaded or if there is no operational link in its immediate downstream to carry its flow. For such systems, resilience is defined as the minimum amount of reduction in the link capacities that would result in the failure of all the outgoing links of an origin node. We show that such networks do not necessarily become more resilient as additional capacity is built in the network. Moreover, when the external inflow does not exceed the network capacity, selective reductions of capacity at certain links can actually help averting the cascading failures, without requiring any change in the local routing policies. This is an attractive feature as it is often easier in practice to reduce the available capacity of some critical links than to add physical capacity or to alter routing policies, e.g., when such policies are determined by social behavior, as in the case of road traffic networks. The results can thus be used for real-time monitoring of distance-to-failure in such networks and devising a feasible course of actions to avert systemic failures., Comment: Accepted to the IEEE Conference on Decision and Control (CDC), 2016

Voltage control plays an important role in the operation of electricity distribution networks, especially when there is a large penetration of renewable energy resources. In this paper, we focus on voltage control through reactive power compensation and study how different information structures affect the control performance. In particular, we first show that using only voltage measurements to determine reactive power compensation is insufficient to maintain voltage in the acceptable range. Then we propose two fully decentralized and robust algorithms by adding additional information, which can stabilize the voltage in the acceptable range. The one with higher complexity can further minimize a cost of reactive power compensation in a particular form. Both of the two algorithms use only local measurements and local variables and require no communication. In addition, the two algorithms are robust against heterogeneous update rates and delays.

We introduce a new class of (dynamical) systems that inherently capture cascading effects (viewed as consequential effects) and are naturally amenable to combinations. We develop an axiomatic general theory around those systems, and guide the endeavor towards an understanding of cascading failure. The theory evolves as an interplay of lattices and fixed points, and its results may be instantiated to commonly studied models of cascade effects. We characterize the systems through their fixed points, and equip them with two operators. We uncover properties of the operators, and express global systems through combinations of local systems. We enhance the theory with a notion of failure, and understand the class of shocks inducing a system to failure. We develop a notion of mu-rank to capture the energy of a system, and understand the minimal amount of effort required to fail a system, termed resilience. We deduce a dual notion of fragility and show that the combination of systems sets a limit on the amount of fragility inherited., Comment: 31 pages