arXiv subjects

Dileep Kalathil

Publications and source records attributed to Dileep Kalathil.

At least 73 records · Page 4Linked to original sources

arXiv2021

Reinforcement Learning for Mean Field Games with Strategic Complementarities

Mean Field Games (MFG) are the class of games with a very large number of agents and the standard equilibrium concept is a Mean Field Equilibrium (MFE). Algorithms for learning MFE in dynamic MFGs are unknown in general. Our focus is on an important subclass that possess a monotonicity property called Strategic Complementarities (MFG-SC). We introduce a natural refinement to the equilibrium concept that we call Trembling-Hand-Perfect MFE (T-MFE), which allows agents to employ a measure of randomization while accounting for the impact of such randomization on their payoffs. We propose a simple algorithm for computing T-MFE under a known model. We also introduce a model-free and a model-based approach to learning T-MFE and provide sample complexities of both algorithms. We also develop a fully online learning scheme that obviates the need for a simulator. Finally, we empirically evaluate the performance of the proposed algorithms via examples motivated by real-world applications.

math.OC↗

arXiv2020

Bounded Regret for Finitely Parameterized Multi-Armed Bandits

We consider the problem of finitely parameterized multi-armed bandits where the model of the underlying stochastic environment can be characterized based on a common unknown parameter. The true parameter is unknown to the learning agent. However, the set of possible parameters, which is finite, is known a priori. We propose an algorithm that is simple and easy to implement, which we call Finitely Parameterized Upper Confidence Bound (FP-UCB) algorithm, which uses the information about the underlying parameter set for faster learning. In particular, we show that the FP-UCB algorithm achieves a bounded regret under some structural condition on the underlying parameter set. We also show that, if the underlying parameter set does not satisfy the necessary structural condition, the FP-UCB algorithm achieves a logarithmic regret, but with a smaller preceding constant compared to the standard UCB algorithm. We also validate the superior performance of the FP-UCB algorithm through extensive numerical simulations.

cs.LG↗

arXiv2020

A Vision-Based Control Method for Autonomous Landing of Vertical Flight Aircraft On a Moving Platform Without Using GPS

The paper discusses a novel vision-based estimation and control approach to enable fully autonomous tracking and landing of vertical take-off and landing (VTOL) capable unmanned aerial vehicles (UAVs) on moving platforms without relying on a GPS signal. A unique feature of the present method is that it accomplishes this task without tracking the landing pad itself; however, by utilizing a standardized visual cue installed normal to the landing pad and parallel to the pilot's/vehicle's line of sight. A computer vision system using a single monocular camera is developed to detect the visual cue and then accurately estimate the heading of the UAV and its relative distances in all three directions to the landing pad. Through comparison with a Vicon-based motion capture system, the capability of the present vision system to measure distances in real-time within an accuracy of less than a centimeter and heading within a degree with the right visual cue, is demonstrated. A gain-scheduled proportional integral derivative (PID) control system is integrated with the vision system and then implemented on a quad-rotor-UAV dynamic model in a realistic simulation program called Gazebo. Extensive simulations are conducted to demonstrate the ability of the controller to achieve robust tracking and landing on platforms moving in arbitrary trajectories. Repeated flight tests, using both stationary and moving platforms are successfully conducted with less than 5 centimeters of landing error.

cs.RO↗

arXiv2020

Selling Demand Response Using Options

Wholesale electricity markets in many jurisdictions use a two-settlement structure: a day-ahead market for bulk power transactions and a real-time market for fine-grain supply-demand balancing. This paper explores trading demand response assets within this two-settlement market structure. We consider two approaches for trading demand response assets: (a) an intermediate spot market with contingent pricing, and (b) an over-the-counter options contract. In the first case, we characterize the competitive equilibrium of the spot market, and show that it is socially optimal. Economic orthodoxy advocates spot markets, but these require expensive infrastructure and regulatory blessing. In the second case, we characterize competitive equilibria and compare its efficiency with the idealized spot market. Options contract are private bilateral over-the-counter transactions and do not require regulatory approval. We show that the optimal social welfare is, in general, not supported. We then design optimal option prices that minimize the social welfare gap. This optimal design serves to approximate the ideal spot market for demand response using options with modest loss of efficiency. Our results are validated through numerical simulations.

eess.SY↗

arXiv2020

QFlow: A Learning Approach to High QoE Video Streaming at the Wireless Edge

The predominant use of wireless access networks is for media streaming applications, which are only gaining popularity as ever more devices become available for this purpose. However, current access networks treat all packets identically, and lack the agility to determine which clients are most in need of service at a given time. Software reconfigurability of networking devices has seen wide adoption, and this in turn implies that agile control policies can be now instantiated on access networks. The goal of this work is to design, develop and demonstrate QFlow, a learning approach to create a value chain from the application on one side, to algorithms operating over reconfigurable infrastructure on the other, so that applications are able to obtain necessary resources for optimal performance. Using YouTube video streaming as an example, we illustrate how QFlow is able to adaptively provide such resources and attain a high QoE for all clients at a wireless access point.

cs.LG↗

arXiv2020

Creation of Synthetic Networked PMU Data: A Generative Adversarial Network Approach

This paper introduces a machine learning-based approach to synthetically creating realistic phasor measurement unit (PMU) data streams of multiple transient types. In contrast to the existing literature of transient simulation-based data generation methods, we propose a generative adversarial network (GAN) based approach to learning directly from the historical data and simultaneously reproduce multiple PMU data streams. The synthetic PMU data streams reflect meaningful dynamic characteristics which observe first principles such as Kirchhoff's laws. The efficacy of this approach is demonstrated by numerical studies on the IEEE 39-bus system. We validate the fidelity and flexibility of the synthetic data via statistical resemblance and modal analysis approaches. Finally we illustrate a practical application scenario for the usage of the synthetic PMU data, i.e. leverage the synthetic data to improve the performance of the event classification algorithms.

eess.SP↗

arXiv2020

Learning to Cache and Caching to Learn: Regret Analysis of Caching Algorithms

Crucial performance metrics of a caching algorithm include its ability to quickly and accurately learn a popularity distribution of requests. However, a majority of work on analytical performance analysis focuses on hit probability after an asymptotically large time has elapsed. We consider an online learning viewpoint, and characterize the "regret" in terms of the finite time difference between the hits achieved by a candidate caching algorithm with respect to a genie-aided scheme that places the most popular items in the cache. We first consider the Full Observation regime wherein all requests are seen by the cache. We show that the Least Frequently Used (LFU) algorithm is able to achieve order optimal regret, which is matched by an efficient counting algorithm design that we call LFU-Lite. We then consider the Partial Observation regime wherein only requests for items currently cached are seen by the cache, making it similar to an online learning problem related to the multi-armed bandit problem. We show how approaching this "caching bandit" using traditional approaches yields either high complexity or regret, but a simple algorithm design that exploits the structure of the distribution can ensure order optimal regret. We conclude by illustrating our insights using numerical simulations.

cs.NI↗

arXiv2020

D2C 2.0: Decoupled Data-Based Approach for Learning to Control Stochastic Nonlinear Systems via Model-Free ILQR

In this paper, we propose a structured linear parameterization of a feedback policy to solve the model-free stochastic optimal control problem. This parametrization is corroborated by a decoupling principle that is shown to be near-optimal under a small noise assumption, both in theory and by empirical analyses. Further, we incorporate a model-free version of the Iterative Linear Quadratic Regulator (ILQR) in a sample-efficient manner into our framework. Simulations on systems over a range of complexities reveal that the resulting algorithm is able to harness the superior second-order convergence properties of ILQR. As a result, it is fast and is scalable to a wide variety of higher dimensional systems. Comparisons are made with a state-of-the-art reinforcement learning algorithm, the Deep Deterministic Policy Gradient (DDPG) technique, in order to demonstrate the significant merits of our approach in terms of training-efficiency.

math.OC↗

arXiv2019

Nested Reinforcement Learning Based Control for Protective Relays in Power Distribution Systems

This paper envisions a new control architecture for the protective relay setting in future power distribution systems. With deepening penetration of distributed energy resources at the end users level, it has been recognized as a key engineering challenge to redesign the protective relays in the future distribution system. Conceptually, these protective relays are the discrete ON/OFF control devices at the end of each branch and node in a power network. The key technical difficulty lies in how to set up the relay control logic so that the protection could successfully differentiate heavy load and faulty operating conditions. This paper proposes a new nested reinforcement learning approach to take advantage of the structural properties of distribution networks and develop a new set of training methods for tuning the protective relays.

eess.SY↗

arXiv2019

Mechanism Design for Demand Response Programs

Demand Response (DR) programs serve to reduce the consumption of electricity at times when the supply is scarce and expensive. The utility informs the aggregator of an anticipated DR event. The aggregator calls on a subset of its pool of recruited agents to reduce their electricity use. Agents are paid for reducing their energy consumption from contractually established baselines. Baselines are counter-factual consumption estimates of the energy an agent would have consumed if they were not participating in the DR program. Baselines are used to determine payments to agents. This creates an incentive for agents to inflate their baselines. We propose a novel self-reported baseline mechanism (SRBM) where each agent reports its baseline and marginal utility. These reports are strategic and need not be truthful. Based on the reported information, the aggregator selects or calls on agents to meet the load reduction target. Called agents are paid for observed reductions from their self-reported baselines. Agents who are not called face penalties for consumption shortfalls below their baselines. The mechanism is specified by the probability with which agents are called, reward prices for called agents, and penalty prices for agents who are not called. Under SRBM, we show that truthful reporting of baseline consumption and marginal utility is a dominant strategy. Thus, SRBM eliminates the incentive for agents to inflate baselines. SRBM is assured to meet the load reduction target. SRBM is also nearly efficient since it selects agents with the smallest marginal utilities, and each called agent contributes maximally to the load reduction target. Finally, we show that SRBM is almost optimal in the metric of average cost of DR provision faced by the aggregator.

cs.GT↗

arXiv2019

Decoupled Data Based Approach for Learning to Control Nonlinear Dynamical Systems

This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical system with continuous state space, continuous action space and unknown dynamics. This class of problems are typically addressed in stochastic adaptive control and reinforcement learning literature using model-based and model-free approaches respectively. Both methods rely on solving a dynamic programming problem, either directly or indirectly, for finding the optimal closed loop control policy. The inherent `curse of dimensionality' associated with dynamic programming method makes these approaches also computationally difficult. This paper proposes a novel decoupled data-based control (D2C) algorithm that addresses this problem using a decoupled, `open loop - closed loop', approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, a closed loop control is developed around this open loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests significant reduction in training time compared to other state of the art algorithms.

cs.LG↗

arXiv2019

Empirical Q-Value Iteration

We propose a new simple and natural algorithm for learning the optimal Q-value function of a discounted-cost Markov Decision Process (MDP) when the transition kernels are unknown. Unlike the classical learning algorithms for MDPs, such as Q-learning and actor-critic algorithms, this algorithm doesn't depend on a stochastic approximation-based method. We show that our algorithm, which we call the empirical Q-value iteration (EQVI) algorithm, converges to the optimal Q-value function. We also give a rate of convergence or a non-asymptotic sample complexity bound, and also show that an asynchronous (or online) version of the algorithm will also work. Preliminary experimental results suggest a faster rate of convergence to a ball park estimate for our algorithm compared to stochastic approximation-based algorithms.

math.OC↗

arXiv2019

FlowBazaar: A Market-Mediated Software Defined Communications Ecosystem at the Wireless Edge

The predominant use of wireless access networks is for media streaming applications, which are only gaining popularity as ever more devices become available for this purpose. However, current access networks treat all packets identically, and lack the agility to determine which clients are most in need of service at a given time. Software reconfigurability of networking devices has seen wide adoption, and this in turn implies that agile control policies can be now instantiated on access networks. The goal of this work is to design, develop and demonstrate FlowBazaar, an market-based approach to create a value chain from the application on one side, to algorithms operating over reconfigurable infrastructure on the other, so that applications are able to obtain necessary resources for optimal performance. Using YouTube video streaming as an example, we illustrate how FlowBazaar is able to adaptively provide such resources and attain a high QoE for all clients at a wireless access point.

cs.NI↗

arXiv2018

Estimating Phase Duration for SPaT Messages

A SPaT (Signal Phase and Timing) message describes for each lane the current phase at a signalized intersection together with an estimate of the residual time of that phase. Accurate SPaT messages can be used to construct a speed profile for a vehicle that reduces its fuel consumption as it approaches or leaves an intersection. This paper presents SPaT estimation algorithms at an intersection with a semi-actuated signal, using real-time signal phase measurements. The algorithms are evaluated using high-resolution data from two intersections in Montgomery County, MD. The algorithms can be readily implemented at signal controllers. The study supports three findings. First, real-time information dramatically improves the accuracy of the prediction of the residual time compared with prediction based on historical data alone. Second, as time increases the prediction of the residual time may increase or decrease. Third, as drivers differently weight errors in predicting `end of green' and `end of red', drivers on two different approaches may prefer different estimates of the residual time of the same phase.

stat.AP↗

arXiv2016

On Regret-Optimal Learning in Decentralized Multi-player Multi-armed Bandits

We consider the problem of learning in single-player and multiplayer multiarmed bandit models. Bandit problems are classes of online learning problems that capture exploration versus exploitation tradeoffs. In a multiarmed bandit model, players can pick among many arms, and each play of an arm generates an i.i.d. reward from an unknown distribution. The objective is to design a policy that maximizes the expected reward over a time horizon for a single player setting and the sum of expected rewards for the multiplayer setting. In the multiplayer setting, arms may give different rewards to different players. There is no separate channel for coordination among the players. Any attempt at communication is costly and adds to regret. We propose two decentralizable policies, $\tt E^3$ ($\tt E$-$\tt cubed$) and $\tt E^3$-$\tt TS$, that can be used in both single player and multiplayer settings. These policies are shown to yield expected regret that grows at most as O($\log^{1+ε} T$). It is well known that $\log T$ is the lower bound on the rate of growth of regret even in a centralized case. The proposed algorithms improve on prior work where regret grew at O($\log^2 T$). More fundamentally, these policies address the question of additional cost incurred in decentralized online learning, suggesting that there is at most an $ε$-factor cost in terms of order of regret. This solves a problem of relevance in many domains and had been open for a while.

stat.ML↗

arXiv2016

Optimal Decentralized Control with Asymmetric One-Step Delayed Information Sharing

We consider optimal control of decentralized LQG problems for plants controlled by two players having asymmetric information sharing patterns between them. In one scenario, players are assumed to have a bidirectional error-free, unlimited rate communication channel with no delay in one direction and a unit delay in the other. In another scenario, the communication channel is assumed to be unidirectional with a unit delay. Delayed information sharing patterns in general do not admit linear optimal control laws and are thus difficult to control optimally. However, in these scenarios, we show that the problem has a partially nested information structure, and thus linear optimal control laws exist. Summary statistics to characterize these laws are developed and deterministic convex optimization problems are formulated whose solutions yield the optimal control laws. The state feedback case is solved for both scenarios and extended to output and partial output feedback in case of bidirectional and unidirectional channels respectively.

math.OC↗

arXiv2016

The Sharing Economy for the Smart Grid

The sharing economy has disrupted housing and transportation sectors. Homeowners can rent out their property when they are away on vacation, car owners can offer ride sharing services. These sharing economy business models are based on monetizing under-utilized infrastructure. They are enabled by peer-to-peer platforms that match eager sellers with willing buyers. Are there compelling sharing economy opportunities in the electricity sector? What products or services can be shared in tomorrow's Smart Grid? We begin by exploring sharing economy opportunities in the electricity sector, and discuss regulatory and technical obstacles to these opportunities. We then study the specific problem of a collection of firms sharing their electricity storage. We characterize equilibrium prices for shared storage in a spot market. We formulate storage investment decisions of the firms as a non-convex non-cooperative game. We show that under a mild alignment condition, a Nash equilibrium exists, it is unique, and it supports the social welfare. We discuss technology platforms necessary for the physical exchange of power, and market platforms necessary to trade electricity storage. We close with synthetic examples to illustrate our ideas.

eess.SY↗

arXiv2016

Approachability in Stackelberg Stochastic Games with Vector Costs

The notion of approachability was introduced by Blackwell [1] in the context of vector-valued repeated games. The famous Blackwell's approachability theorem prescribes a strategy for approachability, i.e., for `steering' the average cost of a given agent towards a given target set, irrespective of the strategies of the other agents. In this paper, motivated by the multi-objective optimization/decision making problems in dynamically changing environments, we address the approachability problem in Stackelberg stochastic games with vector valued cost functions. We make two main contributions. Firstly, we give a simple and computationally tractable strategy for approachability for Stackelberg stochastic games along the lines of Blackwell's. Secondly, we give a reinforcement learning algorithm for learning the approachable strategy when the transition kernel is unknown. We also recover as a by-product Blackwell's necessary and sufficient condition for approachability for convex sets in this set up and thus a complete characterization. We also give sufficient conditions for non-convex sets.

cs.LG↗