arXiv subjects

Shalabh Bhatnagar

Publications and source records attributed to Shalabh Bhatnagar.

At least 73 records · Page 4Linked to original sources

arXiv2019

A unified decision making framework for supply and demand management in microgrid networks

This paper considers two important problems -- on the supply-side and demand-side respectively and studies both in a unified framework. On the supply side, we study the problem of energy sharing among microgrids with the goal of maximizing profit obtained from selling power while at the same time not deviating much from the customer demand. On the other hand, under shortage of power, this problem becomes one of deciding the amount of power to be bought with dynamically varying prices. On the demand side, we consider the problem of optimally scheduling the time-adjustable demand - i.e., of loads with flexible time windows in which they can be scheduled. While previous works have treated these two problems in isolation, we combine these problems together and provide a unified Markov decision process (MDP) framework for these problems. We then apply the Q-learning algorithm, a popular model-free reinforcement learning technique, to obtain the optimal policy. Through simulations, we show that the policy obtained by solving our MDP model provides more profit to the microgrids.

eess.SY↗

arXiv2019

Successive Over Relaxation Q-Learning

In a discounted reward Markov Decision Process (MDP), the objective is to find the optimal value function, i.e., the value function corresponding to an optimal policy. This problem reduces to solving a functional equation known as the Bellman equation and a fixed point iteration scheme known as the value iteration is utilized to obtain the solution. In literature, a successive over-relaxation based value iteration scheme is proposed to speed-up the computation of the optimal value function. The speed-up is achieved by constructing a modified Bellman equation that ensures faster convergence to the optimal value function. However, in many practical applications, the model information is not known and we resort to Reinforcement Learning (RL) algorithms to obtain optimal policy and value function. One such popular algorithm is Q-learning. In this paper, we propose Successive Over-Relaxation (SOR) Q-learning. We first derive a modified fixed point iteration for SOR Q-values and utilize stochastic approximation to derive a learning algorithm to compute the optimal value function and an optimal policy. We then prove the almost sure convergence of the SOR Q-learning to SOR Q-values. Finally, through numerical experiments, we show that SOR Q-learning is faster compared to the standard Q-learning algorithm.

cs.LG↗

arXiv2019

An Online Sample Based Method for Mode Estimation using ODE Analysis of Stochastic Approximation Algorithms

One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function is known, mode is an argument of the maximum value of the density function and one can apply the optimization techniques to find mode. In many of the practical applications, the analytical form of the density is not known and only the samples from the distribution are available. Most of the techniques proposed in the literature for estimating the mode from the samples assume that all the samples are available beforehand. Moreover, some of the techniques employ computationally expensive operations like sorting. In this work we provide a computationally effective, on-line iterative algorithm that estimates the mode of a unimodal smooth density given only the samples generated from the density. Asymptotic convergence of the proposed algorithm using an ordinary differential equation (ODE) based analysis is provided. We also prove the stability of estimates by utilizing the concept of regularization. Experimental results further demonstrate the effectiveness of the proposed algorithm.

cs.LG↗

arXiv2019

Learning Active Spine Behaviors for Dynamic and Efficient Locomotion in Quadruped Robots

In this work, we provide a simulation framework to perform systematic studies on the effects of spinal joint compliance and actuation on bounding performance of a 16-DOF quadruped spined robot Stoch 2. Fast quadrupedal locomotion with active spine is an extremely hard problem, and involves a complex coordination between the various degrees of freedom. Therefore, past attempts at addressing this problem have not seen much success. Deep-Reinforcement Learning seems to be a promising approach, after its recent success in a variety of robot platforms, and the goal of this paper is to use this approach to realize the aforementioned behaviors. With this learning framework, the robot reached a bounding speed of 2.1 m/s with a maximum Froude number of 2. Simulation results also show that use of active spine, indeed, increased the stride length, improved the cost of transport, and also reduced the natural frequency to more realistic values.

cs.RO↗

arXiv2019

Asynchronous stochastic approximations with asymptotically biased errors and deep multi-agent learning

Asynchronous stochastic approximations (SAs) are an important class of model-free algorithms, tools and techniques that are popular in multi-agent and distributed control scenarios. To counter Bellman's curse of dimensionality, such algorithms are coupled with function approximations. Although the learning/ control problem becomes more tractable, function approximations affect stability and convergence. In this paper, we present verifiable sufficient conditions for stability and convergence of asynchronous SAs with biased approximation errors. The theory developed herein is used to analyze Policy Gradient methods and noisy Value Iteration schemes. Specifically, we analyze the asynchronous approximate counterparts of the policy gradient (A2PG) and value iteration (A2VI) schemes. It is shown that the stability of these algorithms is unaffected by biased approximation errors, provided they are asymptotically bounded. With respect to convergence (of A2VI and A2PG), a relationship between the limiting set and the approximation errors is established. Finally, experimental results are presented that support the theory.

math.OC↗

arXiv2019

Random directions stochastic approximation with deterministic perturbations

We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order algorithms to incorporate deterministic perturbations. We show that the gradient and/or Hessian estimates in the resulting algorithms with deterministic perturbations are asymptotically unbiased, so that the algorithms are provably convergent. Furthermore, we derive convergence rates to establish the superiority of the first-order and second-order algorithms, for the special case of a convex and quadratic optimization problem, respectively. Numerical experiments are used to validate the theoretical results.

math.OC↗

arXiv2019

Design, Development and Experimental Realization of a Quadrupedal Research Platform: Stoch

In this paper, we present a complete description of the hardware design and control architecture of our custom built quadruped robot, called the `Stoch'. Our goal is to realize a robust, modular, and a reliable quadrupedal platform, using which various locomotion behaviors are explored. This platform enables us to explore different research problems in legged locomotion, which use both traditional and learning based techniques. We discuss the merits and limitations of the platform in terms of exploitation of available behaviours, fast rapid prototyping, reproduction and repair. Towards the end, we will demonstrate trotting, bounding behaviors, and preliminary results in turning. In addition, we will also show various gait transitions i.e., trot-to-turn and trot-to-bound behaviors.

cs.RO↗

arXiv2019

Realizing Learned Quadruped Locomotion Behaviors through Kinematic Motion Primitives

Humans and animals are believed to use a very minimal set of trajectories to perform a wide variety of tasks including walking. Our main objective in this paper is two fold 1) Obtain an effective tool to realize these basic motion patterns for quadrupedal walking, called the kinematic motion primitives (kMPs), via trajectories learned from deep reinforcement learning (D-RL) and 2) Realize a set of behaviors, namely trot, walk, gallop and bound from these kinematic motion primitives in our custom four legged robot, called the `Stoch'. D-RL is a data driven approach, which has been shown to be very effective for realizing all kinds of robust locomotion behaviors, both in simulation and in experiment. On the other hand, kMPs are known to capture the underlying structure of walking and yield a set of derived behaviors. We first generate walking gaits from D-RL, which uses policy gradient based approaches. We then analyze the resulting walking by using principal component analysis. We observe that the kMPs extracted from PCA followed a similar pattern irrespective of the type of gaits generated. Leveraging on this underlying structure, we then realize walking in Stoch by a straightforward reconstruction of joint trajectories from kMPs. This type of methodology improves the transferability of these gaits to real hardware, lowers the computational overhead on-board, and also avoids multiple training iterations by generating a set of derived behaviors from a single learned gait.

cs.RO↗

arXiv2019

Dynamics of stochastic approximation with iterate-dependent Markov noise under verifiable conditions in compact state space with the stability of iterates not ensured

This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability (i.e. the probability of convergence of the iterates to a specific attractor of the limiting o.d.e. given that the iterates are in its domain of attraction after a sufficiently large number of iterations (say) n 0 ) framework to such recursions. Specifically, with the more restrictive assumption of Markov iterate-dependent noise supported on a bounded subset of the Euclidean space we give a lower bound for the lock-in probability. We use these results to prove almost sure convergence of the iterates to the specified attractor when the iterates satisfy an asymptotic tightness condition. The novelty of our approach is that if the state space of the Markov process is compact we prove almost sure convergence under much weaker assumptions compared to the work by Andrieu et al. which solves the general state space case under much restrictive assumptions. We also extend our single timescale results to the case where there are two separate recursions over two different timescales. This, in turn, is shown to be useful in analyzing the tracking ability of general adaptive algorithms. Additionally, we show that our results can be used to derive a sample complexity estimate of such recursions, which then can be used for step-size selection

math.DS↗

arXiv2018

Memory-based Deep Reinforcement Learning for Obstacle Avoidance in UAV with Limited Environment Knowledge

This paper presents our method for enabling a UAV quadrotor, equipped with a monocular camera, to autonomously avoid collisions with obstacles in unstructured and unknown indoor environments. When compared to obstacle avoidance in ground vehicular robots, UAV navigation brings in additional challenges because the UAV motion is no more constrained to a well-defined indoor ground or street environment. Horizontal structures in indoor and outdoor environments like decorative items, furnishings, ceiling fans, sign-boards, tree branches etc., also become relevant obstacles unlike those for ground vehicular robots. Thus, methods of obstacle avoidance developed for ground robots are clearly inadequate for UAV navigation. Current control methods using monocular images for UAV obstacle avoidance are heavily dependent on environment information. These controllers do not fully retain and utilize the extensively available information about the ambient environment for decision making. We propose a deep reinforcement learning based method for UAV obstacle avoidance (OA) and autonomous exploration which is capable of doing exactly the same. The crucial idea in our method is the concept of partial observability and how UAVs can retain relevant information about the environment structure to make better future navigation decisions. Our OA technique uses recurrent neural networks with temporal attention and provides better results compared to prior works in terms of distance covered during navigation without collisions. In addition, our technique has a high inference rate (a key factor in robotic applications) and is energy-efficient as it minimizes oscillatory motion of UAV and reduces power wastage.

cs.RO↗

arXiv2018

Generalized Deterministic Perturbations For Stochastic Gradient Search

Stochastic optimization (SO) considers the problem of optimizing an objective function in the presence of noise. Most of the solution techniques in SO estimate gradients from the noise corrupted observations of the objective and adjust parameters of the objective along the direction of the estimated gradients to obtain locally optimal solutions. Two prominent algorithms in SO namely Random Direction Kiefer-Wolfowitz (RDKW) and Simultaneous Perturbation Stochastic Approximation (SPSA) obtain noisy gradient estimate by randomly perturbing all the parameters simultaneously. This forces the search direction to be random in these algorithms and causes them to suffer additional noise on top of the noise incurred from the samples of the objective. Owing to this additional noise, the idea of using deterministic perturbations instead of random perturbations for gradient estimation has also been studied. Two specific constructions of the deterministic perturbation sequence using lexicographical ordering and Hadamard matrices have been explored and encouraging results have been reported in the literature. In this paper, we characterize the class of deterministic perturbation sequences that can be utilized in the RDKW algorithm. This class expands the set of known deterministic perturbation sequences available in the literature. Using our characterization we propose a construction of a deterministic perturbation sequence that has the least possible cycle length among all deterministic perturbations. Through simulations we illustrate the performance gain of the proposed deterministic perturbation sequence in the RDKW algorithm over the Hadamard and the random perturbation counterparts. We establish the convergence of the RDKW algorithm for the generalized class of deterministic perturbations.

eess.SY↗

arXiv2018

An Online Prediction Algorithm for Reinforcement Learning with Linear Function Approximation using Cross Entropy Method

In this paper, we provide two new stable online algorithms for the problem of prediction in reinforcement learning, \emph{i.e.}, estimating the value function of a model-free Markov reward process using the linear function approximation architecture and with memory and computation costs scaling quadratically in the size of the feature set. The algorithms employ the multi-timescale stochastic approximation variant of the very popular cross entropy (CE) optimization method which is a model based search method to find the global optimum of a real-valued function. A proof of convergence of the algorithms using the ODE method is provided. We supplement our theoretical results with experimental comparisons. The algorithms achieve good performance fairly consistently on many RL benchmark problems with regards to computational efficiency, accuracy and stability.

cs.LG↗

arXiv2018

Stability of Stochastic Approximations with `Controlled Markov' Noise and Temporal Difference Learning

We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a `controlled Markov' process. Analyzing this class of algorithms is important, since many reinforcement learning (RL) algorithms can be cast as SAs driven by a `controlled Markov' process. In this paper, we present easily verifiable sufficient conditions for stability and convergence of SAs driven by a `controlled Markov' process. Many RL applications involve continuous state spaces. While our analysis readily ensures stability for such continuous state applications, traditional analyses do not. As compared to literature, our analysis presents a two-fold generalization (a) the Markov process may evolve in a continuous state space and (b) the process need not be ergodic under any given stationary policy. Temporal difference learning (TD) is an important policy evaluation method in reinforcement learning. The theory developed herein, is used to analyze generalized $TD(0)$, an important variant of TD. Our theory is also used to analyze a TD formulation of supervised learning for forecasting problems.

eess.SY↗

arXiv2018

Novel Sensor Scheduling Scheme for Intruder Tracking in Energy Efficient Sensor Networks

We consider the problem of tracking an intruder using a network of wireless sensors. For tracking the intruder at each instant, the optimal number and the right configuration of sensors has to be powered. As powering the sensors consumes energy, there is a trade off between accurately tracking the position of the intruder at each instant and the energy consumption of sensors. This problem has been formulated in the framework of Partially Observable Markov Decision Process (POMDP). Even for the state-of-the-art algorithm in the literature, the curse of dimensionality renders the problem intractable. In this paper, we formulate the Intrusion Detection (ID) problem with a suitable state-action space in the framework of POMDP and develop a Reinforcement Learning (RL) algorithm utilizing the Upper Confidence Tree Search (UCT) method to solve the ID problem. Through simulations, we show that our algorithm performs and scales well with the increasing state and action spaces.

cs.AI↗

arXiv2018

On Continuous-space Embedding of Discrete-parameter Queueing Systems

Motivated by the problem of discrete-parameter simulation optimization (DPSO) of queueing systems, we consider the problem of embedding the discrete parameter space into a continuous one so that descent-based continuous-space methods could be directly applied for efficient optimization. We show that a randomization of the simulation model itself can be used to achieve such an embedding when the objective function is a long-run average measure. Unlike spatial interpolation, the computational cost of this embedding is independent of the number of parameters in the system, making the approach ideally suited to high-dimensional problems. We describe in detail the application of this technique to discrete-time queues for embedding queue capacities, number of servers and server-delay parameters into continuous space and empirically show that the technique can produce smooth interpolations of the objective function. Through an optimization case-study of a queueing network with $10^7$ design points, we demonstrate that existing continuous optimizers can be effectively applied over such an embedding to find good solutions.

cs.PF↗

arXiv2018

An Incremental Off-policy Search in a Model-free Markov Decision Process Using a Single Sample Path

In this paper, we consider a modified version of the control problem in a model free Markov decision process (MDP) setting with large state and action spaces. The control problem most commonly addressed in the contemporary literature is to find an optimal policy which maximizes the value function, i.e., the long run discounted reward of the MDP. The current settings also assume access to a generative model of the MDP with the hidden premise that observations of the system behaviour in the form of sample trajectories can be obtained with ease from the model. In this paper, we consider a modified version, where the cost function is the expectation of a non-convex function of the value function without access to the generative model. Rather, we assume that a sample trajectory generated using a priori chosen behaviour policy is made available. In this restricted setting, we solve the modified control problem in its true sense, i.e., to find the best possible policy given this limited information. We propose a stochastic approximation algorithm based on the well-known cross entropy method which is data (sample trajectory) efficient, stable, robust as well as computationally and storage efficient. We provide a proof of convergence of our algorithm to a policy which is globally optimal relative to the behaviour policy. We also present experimental results to corroborate our claims and we demonstrate the superiority of the solution produced by our algorithm compared to the state-of-the-art algorithms under appropriately chosen behaviour policy.

cs.AI↗

arXiv2018

A Cross Entropy based Optimization Algorithm with Global Convergence Guarantees

The cross entropy (CE) method is a model based search method to solve optimization problems where the objective function has minimal structure. The Monte-Carlo version of the CE method employs the naive sample averaging technique which is inefficient, both computationally and space wise. We provide a novel stochastic approximation version of the CE method, where the sample averaging is replaced with incremental geometric averaging. This approach can save considerable computational and storage costs. Our algorithm is incremental in nature and possesses additional attractive features such as accuracy, stability, robustness and convergence to the global optimum for a particular class of objective functions. We evaluate the algorithm on a variety of global optimization benchmark problems and the results obtained corroborate our theoretical findings.

cs.AI↗

arXiv2017

RLWS: A Reinforcement Learning based GPU Warp Scheduler

The Streaming Multiprocessors (SMs) of a Graphics Processing Unit (GPU) execute instructions from a group of consecutive threads, called warps. At each cycle, an SM schedules a warp from a group of active warps and can context switch among the active warps to hide various stalls. Hence the performance of warp scheduler is critical to the performance of GPU. Several heuristic warp scheduling algorithms have been proposed which work well only for the situations they are designed for. GPU workloads are becoming very diverse in nature and hence one heuristic may not work for all cases. To work well over a diverse range of workloads, which might exhibit hitherto unseen characteristics, a warp scheduling algorithm must be able to adapt on-line. We propose a Reinforcement Learning based Warp Scheduler (RLWS) which learns to schedule warps based on the current state of the core and the long-term benefits of scheduling actions, adapting not only to different types of workloads, but also to different execution phases in each workload. As the design space involving the state variables and the parameters (such as learning and exploration rates, reward and penalty values) used by RLWS is large, we use Genetic Algorithm to identify the useful subset of state variables and parameter values. We evaluated the proposed RLWS using the GPGPU-SIM simulator on a large number of workloads from the Rodinia, Parboil, CUDA-SDK and GPGPU-SIM benchmark suites and compared with other state-of-the-art warp scheduling methods. Our RL based implementation achieved either the best or very close to the best performance in 80\% of kernels with an average speedup of 1.06x over the Loose Round Robin strategy and 1.07x over the Two-Level strategy.

cs.DC↗