Searcharxiv⌕ Search

arXiv subjects

Quanyan Zhu

Publications and source records attributed to Quanyan Zhu.

At least 181 records · Page 10Linked to original sources
arXiv2021

Fundamental Limitations in Sequential Prediction and Recursive Algorithms: $\mathcal{L}_{p}$ Bounds via an Entropic Analysis

In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the data and/or noises involved, and the derived lower bounds may all be quantified in a conditional entropy characterization. We also study the conditions to achieve the generic bounds from an innovations' viewpoint.

cs.LG↗
arXiv2021

Fundamental Stealthiness-Distortion Tradeoffs in Dynamical Systems under Injection Attacks: A Power Spectral Analysis

In this paper, we analyze the fundamental stealthiness-distortion tradeoffs of linear Gaussian dynamical systems under data injection attacks using a power spectral analysis, whereas the Kullback-Leibler (KL) divergence is employed as the stealthiness measure. Particularly, we obtain explicit formulas in terms of power spectra that characterize analytically the stealthiness-distortion tradeoffs as well as the properties of the worst-case attacks. Furthermore, it is seen in general that the attacker only needs to know the input-output behaviors of the systems in order to carry out the worst-case attacks.

eess.SY↗
arXiv2021

On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment

This paper studies dynamic mechanism design in a quasilinear Markovian environment and analyzes a direct mechanism model of a principal-agent framework in which the agent is allowed to exit at any period. We consider that the agent's private information, referred to as state, evolves over time. The agent makes decisions of whether to stop or continue and what to report at each period. The principal, on the other hand, chooses decision rules consisting of an allocation rule and a set of payment rules to maximize her ex-ante expected payoff. In order to influence the agent's stopping decision, one of the terminal payment rules is posted-price, i.e., it depends only on the realized stopping time of the agent. We define the incentive compatibility in this dynamic environment in terms of Bellman equations, which is then simplified by establishing a one-shot deviation principle. Given the optimality of the stopping rule, a sufficient condition for incentive compatibility is obtained by constructing the state-dependent payment rules in terms of a set of functions parameterized by the allocation rule. A necessary condition is derived from envelope theorem, which explicitly formulates the state-dependent payment rules in terms of allocation rules. A class of monotone environment is considered to characterize the optimal stopping by a threshold rule. The posted-price payment rules are then pinned down in terms of the allocation rule and the threshold function up to a constant. The incentive compatibility constraints restrict the design of the posted-price payment rule by a regular condition.

math.DS↗
arXiv2021

Information-Theoretic Performance Limitations of Feedback Control: Underlying Entropic Laws and Generic $\mathcal{L}_{p}$ Bounds

In this paper, we utilize information theory to study the fundamental performance limitations of generic feedback systems, where both the controller and the plant may be any causal functions/mappings while the disturbance can be with any distributions. More specifically, we obtain fundamental $\mathcal{L}_p$ bounds on the control error, which are shown to be completely characterized by the conditional entropy of the disturbance, based upon the entropic laws that are inherent in any feedback systems. We also discuss the generality and implications (in, e.g., fundamental limits of learning-based control) of the obtained bounds.

eess.SY↗
arXiv2021

Optimal Curing Strategy for Competing Epidemics Spreading over Complex Networks

Optimal curing strategy of suppressing competing epidemics spreading over complex networks is a critical issue. In this paper, we first establish a framework to capture the coupling between two epidemics, and then analyze the system's equilibrium states by categorizing them into three classes, and deriving their stability conditions. The designed curing strategy globally optimizes the trade-off between the curing cost and the severity of epidemics in the network. In addition, we provide structural results on the predictability of epidemic spreading by showing the existence and uniqueness of the solution. We also demonstrate the robustness of curing strategy by showing the continuity of epidemic severity with respect to the applied curing effort. A gradient descent algorithm based on a fixed-point iterative scheme is proposed to find the optimal curing strategy. Depending on the system parameters, the curing strategy can lead to switching between equilibria of the epidemic network as the control cost varies. Finally, we use case studies to corroborate and illustrate the obtained theoretical results.

eess.SY↗
arXiv2021

Cross-Layer Coordinated Attacks on Cyber-Physical Systems: A LQG Game Framework with Controlled Observations

This work establishes a game-theoretic framework to study cross-layer coordinated attacks on cyber-physical systems (CPSs). The attacker can interfere with the physical process and launch jamming attacks on the communication channels simultaneously. At the same time, the defender can dodge the jamming by dispensing with observations. The generic framework captures a wide variety of classic attack models on CPSs. Leveraging dynamic programming techniques, we fully characterize the Subgame Perfect Equilibrium (SPE) control strategies. We also derive the SPE observation and jamming strategies and provide efficient computational methods to compute them. The results demonstrate that the physical and cyber attacks are coordinated and depend on each other. On the one hand, the control strategies are linear in the state estimate, and the estimate error caused by jamming attacks will induce performance degradation. On the other hand, the interactions between the attacker and the defender in the physical layer significantly impact the observation and jamming strategies. Numerical examples illustrate the interactions between the defender and the attacker through their observation and jamming strategies.

eess.SY↗
arXiv2021

Transactive Resilience in Renewable Microgrids: A Contract-Theoretic Approach

Renewable energy-based microgrids play a critical role in future smart grids. Due to the uncertainties of renewable generations, the microgrids face potential risk of load shedding during operation. To address this problem, we propose a contract-based approach to enhance the resilience of microgrids. Specifically, in the framework, the microgrids who may not be self-efficient to meet their local demands can purchase the needed power from their connected microgrids by signing a contract that specifies the power price in advance. We leverage a principal-agent model to capture the energy trading relationships between the microgrids through a resilience as a service (RaaS) paradigm. By focusing on the incentive compatible and individual rational constraints of the service requester, the service provider designs the optimal contracts for the transactive resilience that yields the largest payoff despite the incomplete information. We characterize analytical solutions of the optimal contracts for several scenarios where the service requester has various options on its hidden actions. Numerical simulations are used to illustrate and corroborate the obtained results.

eess.SY↗
arXiv2021

Assets Defending Differential Games with Partial Information and Selected Observations

In this paper, we consider a linear-quadratic-Gaussian defending assets differential game (DADG) where the attacker and the defender do not know each other's state information while they know the trajectory of a moving asset. Both players can choose to observe the other player's state information by paying a cost. The defender and the attacker have to craft both control strategies and observation strategies. We obtain a closed-form feedback solution that characterizes the Nash control strategies. We show that the trajectory of the asset does not affect both players' observation choices. Moreover, we show that the observation choices of the defender and the attacker can be decoupled and the Nash observation strategies can be found by solving two independent optimization problems. A set of necessary conditions is developed to characterize the optimal observation instances. Based on the necessary conditions, an effective algorithm is proposed to numerically compute the optimal observation instances. A case study is presented to demonstrate the effectiveness of the optimal observation instances.

eess.SY↗
arXiv2021

Locally-Aware Constrained Games on Networks

Network games have been instrumental in understanding strategic behaviors over networks for applications such as critical infrastructure networks, social networks, and cyber-physical systems. One critical challenge of network games is that the behaviors of the players are constrained by the underlying physical laws or safety rules, and the players may not have complete knowledge of network-wide constraints. To this end, this paper proposes a game framework to study constrained games on networks, where the players are locally aware of the constraints. We use \textit{awareness levels} to capture the scope of the network constraints that players are aware of. We first define and show the existence of generalized Nash equilibria (GNE) of the game, and point out that higher awareness levels of the players would lead to a larger set of GNE solutions. We use necessary and sufficient conditions to characterize the GNE, and propose the concept of the dual game to show that one can convert a locally-aware constrained game into a two-layer unconstrained game problem. We use linear quadratic games as case studies to corroborate the analytical results, and in particular, show the duality between Bertrand games and Cournot games.%, where each layer comprises an unconstrained game.

eess.SY↗
arXiv2021

Convergence of Bayesian Nash Equilibrium in Infinite Bayesian Games under Discretization

We prove the existence of Bayesian Nash Equilibrium (BNE) of general-sum Bayesian games with continuous types and finite actions under the conditions that the utility functions and the prior type distributions are continuous concerning the players' types. Moreover, there exists a sequence of discretized Bayesian games whose BNE strategies converge weakly to a BNE strategy of the infinite Bayesian game. Our proof establishes a connection between the equilibria of the infinite Bayesian game and those of finite approximations, which leads to an algorithm to construct $\varepsilon$-BNE of infinite Bayesian games by discretizing players' type spaces.

cs.GT↗
arXiv2021

Self-Triggered Markov Decision Processes

In this paper, we study Markov Decision Processes (MDPs) with self-triggered strategies, where the idea of self-triggered control is extended to more generic MDP models. This extension broadens the application of self-triggering policies to a broader range of systems. We study the co-design problems of the control policy and the triggering policy to optimize two pre-specified cost criteria. The first cost criterion is introduced by incorporating a pre-specified update penalty into the traditional MDP cost criteria to reduce the use of communication resources. Under this criteria, a novel dynamic programming (DP) equation called DP equation with optimized lookahead to proposed to solve for the self-triggering policy under this criteria. The second self-triggering policy is to maximize the triggering time while still guaranteeing a pre-specified level of sub-optimality. Theoretical underpinnings are established for the computation and implementation of both policies. Through a gridworld numerical example, we illustrate the two policies' effectiveness in reducing sources consumption and demonstrate the trade-offs between resource consumption and system performance.

eess.SY↗
arXiv2021

Feedback Capacity of Parallel ACGN Channels and Kalman Filter: Power Allocation with Feedback

In this paper, we relate the feedback capacity of parallel additive colored Gaussian noise (ACGN) channels to a variant of the Kalman filter. By doing so, we obtain lower bounds on the feedback capacity of such channels, as well as the corresponding feedback (recursive) coding schemes, which are essentially power allocation policies with feedback, to achieve the bounds. The results are seen to reduce to existing lower bounds in the case of a single ACGN feedback channel, whereas when it comes to parallel additive white Gaussian noise (AWGN) channels with feedback, the recursive coding scheme reduces to a feedback "water-filling" power allocation policy.

cs.IT↗
arXiv2021

On the Equilibrium Elicitation of Markov Games Through Information Design

This work considers a novel information design problem and studies how the craft of payoff-relevant environmental signals solely can influence the behaviors of intelligent agents. The agents' strategic interactions are captured by an incomplete-information Markov game, in which each agent first selects one environmental signal from multiple signal sources as additional payoff-relevant information and then takes an action. There is a rational information designer (designer) who possesses one signal source and aims to control the equilibrium behaviors of the agents by designing the information structure of her signals sent to the agents. An obedient principle is established which states that it is without loss of generality to focus on the direct information design when the information design incentivizes each agent to select the signal sent by the designer, such that the design process avoids the predictions of the agents' strategic selection behaviors. We then introduce the design protocol given a goal of the designer referred to as obedient implementability (OIL) and characterize the OIL in a class of obedient perfect Bayesian Markov Nash equilibria (O-PBME). A new framework for information design is proposed based on an approach of maximizing the optimal slack variables. Finally, we formulate the designer's goal selection problem and characterize it in terms of information design by establishing a relationship between the O-PBME and the Bayesian Markov correlated equilibria, in which we build upon the revelation principle in classic information design in economics. The proposed approach can be applied to elicit desired behaviors of multi-agent systems in competing as well as cooperating settings and be extended to heterogeneous stochastic games in the complete- and the incomplete-information environments.

cs.MA↗
arXiv2021

Relativistic Control: Feedback Control of Relativistic Dynamics

Strictly speaking, Newton's second law of motion is only an approximation of the so-called relativistic dynamics, i.e., Einstein's modification of the second law based on his theory of special relativity. Although the approximation is almost exact when the velocity of the dynamical system is far less than the speed of light, the difference will become larger and larger (and will eventually go to infinity) as the velocity approaches the speed of light. Correspondingly, feedback control of such dynamics should also take this modification into consideration (though it will render the system nonlinear), especially when the velocity is relatively large. Towards this end, we start this note by studying the state-space representation of the relativistic dynamics. We then investigate on how to employ the feedback linearization approach for such relativistic dynamics, based upon which an additional linear controller may then be designed. As such, the feedback linearization together with the linear controller compose the overall relativistic feedback control law. We also provide discussions on, e.g., controllability, state feedback and output feedback, as well as PID control, in the relativistic setting.

eess.SY↗
arXiv2020

Infinite-Horizon Linear-Quadratic-Gaussian Control with Costly Measurements

In this paper, we consider an infinite horizon Linear-Quadratic-Gaussian control problem with controlled and costly measurements. A control strategy and a measurement strategy are co-designed to optimize the trade-off among control performance, actuating costs, and measurement costs. We address the co-design and co-optimization problem by establishing a dynamic programming equation with controlled lookahead. By leveraging the dynamic programming equation, we fully characterize the optimal control strategy and the measurement strategy analytically. The optimal control is linear in the state estimate that depends on the measurement strategy. We prove that the optimal measurement strategy is independent of the measured state and is periodic. And the optimal period length is determined by the cost of measurements and system parameters. We demonstrate the potential application of the co-design and co-optimization problem in an optimal self-triggered control paradigm. Two examples are provided to show the effectiveness of the optimal measurement strategy in reducing the overhead of measurements while keeping the system performance.

eess.SY↗
arXiv2020

Blackwell Online Learning for Markov Decision Processes

This work provides a novel interpretation of Markov Decision Processes (MDP) from the online optimization viewpoint. In such an online optimization context, the policy of the MDP is viewed as the decision variable while the corresponding value function is treated as payoff feedback from the environment. Based on this interpretation, we construct a Blackwell game induced by MDP, which bridges the gap among regret minimization, Blackwell approachability theory, and learning theory for MDP. Specifically, from the approachability theory, we propose 1) Blackwell value iteration for offline planning and 2) Blackwell $Q-$learning for online learning in MDP, both of which are shown to converge to the optimal solution. Our theoretical guarantees are corroborated by numerical experiments.

cs.LG↗