arXiv subjects

Shalabh Bhatnagar

Publications and source records attributed to Shalabh Bhatnagar.

At least 55 records · Page 3Linked to original sources

arXiv2021

Schedule Based Temporal Difference Algorithms

Learning the value function of a given policy from data samples is an important problem in Reinforcement Learning. TD($λ$) is a popular class of algorithms to solve this problem. However, the weights assigned to different $n$-step returns in TD($λ$), controlled by the parameter $λ$, decrease exponentially with increasing $n$. In this paper, we present a $λ$-schedule procedure that generalizes the TD($λ$) algorithm to the case when the parameter $λ$ could vary with time-step. This allows flexibility in weight assignment, i.e., the user can specify the weights assigned to different $n$-step returns by choosing a sequence $\{λ_t\}_{t \geq 1}$. Based on this procedure, we propose an on-policy algorithm - TD($λ$)-schedule, and two off-policy algorithms - GTD($λ$)-schedule and TDC($λ$)-schedule, respectively. We provide proofs of almost sure convergence for all three algorithms under a general Markov noise framework.

cs.LG↗

arXiv2021

Gradient Temporal Difference with Momentum: Stability and Convergence

Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy ball momentum term and provide choice of step size and momentum parameter that ensures almost sure convergence of these algorithms asymptotically. In doing so, we decompose the heavy ball Gradient TD iterates into three separate iterates with different step sizes. We first analyze these iterates under one-timescale SA setting using results from current literature. However, the one-timescale case is restrictive and a more general analysis can be provided by looking at a three-timescale decomposition of the iterates. In the process, we provide the first conditions for stability and convergence of general three-timescale SA. We then prove that the heavy ball Gradient TD algorithm is convergent using our three-timescale SA analysis. Finally, we evaluate these algorithms on standard RL problems and report improvement in performance over the vanilla algorithms.

cs.LG↗

arXiv2021

Dynamic Mirror Descent based Model Predictive Control for Accelerating Robot Learning

Recent works in Reinforcement Learning (RL) combine model-free (Mf)-RL algorithms with model-based (Mb)-RL approaches to get the best from both: asymptotic performance of Mf-RL and high sample-efficiency of Mb-RL. Inspired by these works, we propose a hierarchical framework that integrates online learning for the Mb-trajectory optimization with off-policy methods for the Mf-RL. In particular, two loops are proposed, where the Dynamic Mirror Descent based Model Predictive Control (DMD-MPC) is used as the inner loop Mb-RL to obtain an optimal sequence of actions. These actions are in turn used to significantly accelerate the outer loop Mf-RL. We show that our formulation is generic for a broad class of MPC-based policies and objectives, and includes some of the well-known Mb-Mf approaches. We finally introduce a new algorithm: Mirror-Descent Model Predictive RL (M-DeMoRL), which uses Cross-Entropy Method (CEM) with elite fractions for the inner loop. Our experiments show faster convergence of the proposed hierarchical approach on benchmark MuJoCo tasks. We also demonstrate hardware training for trajectory tracking in a 2R leg and hardware transfer for robust walking in a quadruped. We show that the inner-loop Mb-RL significantly decreases the number of training iterations required in the real system, thereby validating the proposed approach.

cs.RO↗

arXiv2021

Generalized Second Order Value Iteration in Markov Decision Processes

Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive at the optimal solution. Value iteration is a first order method and therefore it may take a large number of iterations to converge to the optimal solution. Successive relaxation is a popular technique that can be applied to solve a fixed point equation. It has been shown in the literature that, under a special structure of the MDP, successive over-relaxation technique computes the optimal value function faster than standard value iteration. In this work, we propose a second order value iteration procedure that is obtained by applying the Newton-Raphson method to the successive relaxation value iteration scheme. We prove the global convergence of our algorithm to the optimal solution asymptotically and show the second order convergence. Through experiments, we demonstrate the effectiveness of our proposed approach.

cs.LG↗

arXiv2021

Analyzing Approximate Value Iteration Algorithms

In this paper, we consider the stochastic iterative counterpart of the value iteration scheme wherein only noisy and possibly biased approximations of the Bellman operator are available. We call this counterpart as the approximate value iteration (AVI) scheme. Neural networks are often used as function approximators, in order to counter Bellman's curse of dimensionality. In this paper, they are used to approximate the Bellman operator. Since neural networks are typically trained using sample data, errors and biases may be introduced. The design of AVI accounts for implementations with biased approximations of the Bellman operator and sampling errors. We present verifiable sufficient conditions under which AVI is stable (almost surely bounded) and converges to a fixed point of the approximate Bellman operator. To ensure the stability of AVI, we present three different yet related sets of sufficient conditions that are based on the existence of an appropriate Lyapunov function. These Lyapunov function based conditions are easily verifiable and new to the literature. The verifiability is enhanced by the fact that a recipe for the construction of the necessary Lyapunov function is also provided. We also show that the stability analysis of AVI can be readily extended to the general case of set-valued stochastic approximations. Finally, we show that AVI can also be used in more general circumstances, i.e., for finding fixed points of contractive set-valued maps.

eess.SY↗

arXiv2021

Attention Actor-Critic algorithm for Multi-Agent Constrained Co-operative Reinforcement Learning

In this work, we consider the problem of computing optimal actions for Reinforcement Learning (RL) agents in a co-operative setting, where the objective is to optimize a common goal. However, in many real-life applications, in addition to optimizing the goal, the agents are required to satisfy certain constraints specified on their actions. Under this setting, the objective of the agents is to not only learn the actions that optimize the common objective but also meet the specified constraints. In recent times, the Actor-Critic algorithm with an attention mechanism has been successfully applied to obtain optimal actions for RL agents in multi-agent environments. In this work, we extend this algorithm to the constrained multi-agent RL setting. The idea here is that optimizing the common goal and satisfying the constraints may require different modes of attention. By incorporating different attention modes, the agents can select useful information required for optimizing the objective and satisfying the constraints separately, thereby yielding better actions. Through experiments on benchmark multi-agent environments, we show the effectiveness of our proposed algorithm.

cs.AI↗

arXiv2020

A Stochastic Game Framework for Efficient Energy Management in Microgrid Networks

We consider the problem of energy management in microgrid networks. A microgrid is capable of generating a limited amount of energy from a renewable resource and is responsible for handling the demands of its dedicated customers. Owing to the variable nature of renewable generation and the demands of the customers, it becomes imperative that each microgrid optimally manages its energy. This involves intelligently scheduling the demands at the customer side, selling (when there is a surplus) and buying (when there is a deficit) the power from its neighboring microgrids depending on its current and future needs. Typically, the transaction of power among the microgrids happens at a pre-decided price by the central grid. In this work, we formulate the problems of demand and battery scheduling, energy trading and dynamic pricing (where we allow the microgrids to decide the price of the transaction depending on their current configuration of demand and renewable energy) in the framework of stochastic games. Subsequently, we propose a novel approach that makes use of independent learners Deep Q-learning algorithm to solve this problem. Through extensive empirical evaluation, we show that our proposed framework is more beneficial to the majority of the microgrids and we provide a detailed analysis of the results.

eess.SY↗

arXiv2020

Robust Quadrupedal Locomotion on Sloped Terrains: A Linear Policy Approach

In this paper, with a view toward fast deployment of locomotion gaits in low-cost hardware, we use a linear policy for realizing end-foot trajectories in the quadruped robot, Stoch $2$. In particular, the parameters of the end-foot trajectories are shaped via a linear feedback policy that takes the torso orientation and the terrain slope as inputs. The corresponding desired joint angles are obtained via an inverse kinematics solver and tracked via a PID control law. Augmented Random Search, a model-free and a gradient-free learning algorithm is used to train this linear policy. Simulation results show that the resulting walking is robust to terrain slope variations and external pushes. This methodology is not only computationally light-weight but also uses minimal sensing and actuation capabilities in the robot, thereby justifying the approach.

cs.RO↗

arXiv2020

Hindsight Experience Replay with Kronecker Product Approximate Curvature

Hindsight Experience Replay (HER) is one of the efficient algorithm to solve Reinforcement Learning tasks related to sparse rewarded environments.But due to its reduced sample efficiency and slower convergence HER fails to perform effectively. Natural gradients solves these challenges by converging the model parameters better. It avoids taking bad actions that collapse the training performance. However updating parameters in neural networks requires expensive computation and thus increase in training time. Our proposed method solves the above mentioned challenges with better sample efficiency and faster convergence with increased success rate. A common failure mode for DDPG is that the learned Q-function begins to dramatically overestimate Q-values, which then leads to the policy breaking, because it exploits the errors in the Q-function. We solve this issue by including Twin Delayed Deep Deterministic Policy Gradients(TD3) in HER. TD3 learns two Q-functions instead of one and it adds noise tothe target action, to make it harder for the policy to exploit Q-function errors. The experiments are done with the help of OpenAis Mujoco environments. Results on these environments show that our algorithm (TDHER+KFAC) performs better inmost of the scenarios

cs.LG↗

arXiv2020

A reinforcement learning approach to hybrid control design

In this paper we design hybrid control policies for hybrid systems whose mathematical models are unknown. Our contributions are threefold. First, we propose a framework for modelling the hybrid control design problem as a single Markov Decision Process (MDP). This result facilitates the application of off-the-shelf algorithms from Reinforcement Learning (RL) literature towards designing optimal control policies. Second, we model a set of benchmark examples of hybrid control design problem in the proposed MDP framework. Third, we adapt the recently proposed Proximal Policy Optimisation (PPO) algorithm for the hybrid action space and apply it to the above set of problems. It is observed that in each case the algorithm converges and finds the optimal policy.

eess.SY↗

arXiv2020

Learning Stable Manoeuvres in Quadruped Robots from Expert Demonstrations

With the research into development of quadruped robots picking up pace, learning based techniques are being explored for developing locomotion controllers for such robots. A key problem is to generate leg trajectories for continuously varying target linear and angular velocities, in a stable manner. In this paper, we propose a two pronged approach to address this problem. First, multiple simpler policies are trained to generate trajectories for a discrete set of target velocities and turning radius. These policies are then augmented using a higher level neural network for handling the transition between the learned trajectories. Specifically, we develop a neural network-based filter that takes in target velocity, radius and transforms them into new commands that enable smooth transitions to the new trajectory. This transformation is achieved by learning from expert demonstrations. An application of this is the transformation of a novice user's input into an expert user's input, thereby ensuring stable manoeuvres regardless of the user's experience. Training our proposed architecture requires much less expert demonstrations compared to standard neural network architectures. Finally, we demonstrate experimentally these results in the in-house quadruped Stoch 2.

cs.RO↗

arXiv2020

Actor-Critic Algorithms for Constrained Multi-agent Reinforcement Learning

In cooperative stochastic games multiple agents work towards learning joint optimal actions in an unknown environment to achieve a common goal. In many real-world applications, however, constraints are often imposed on the actions that can be jointly taken by the agents. In such scenarios the agents aim to learn joint actions to achieve a common goal (minimizing a specified cost function) while meeting the given constraints (specified via certain penalty functions). In this paper, we consider the relaxation of the constrained optimization problem by constructing the Lagrangian of the cost and penalty functions. We propose a nested actor-critic solution approach to solve this relaxed problem. In this approach, an actor-critic scheme is employed to improve the policy for a given Lagrange parameter update on a faster timescale as in the classical actor-critic architecture. A meta actor-critic scheme using this faster timescale policy updates is then employed to improve the Lagrange parameters on the slower timescale. Utilizing the proposed nested actor-critic schemes, we develop three Nested Actor-Critic (N-AC) algorithms. Through experiments on constrained cooperative tasks, we show the effectiveness of the proposed algorithms.

cs.MA↗

arXiv2020

Reinforcement Learning in Non-Stationary Environments

Reinforcement learning (RL) methods learn optimal decisions in the presence of a stationary environment. However, the stationary assumption on the environment is very restrictive. In many real world problems like traffic signal control, robotic applications, one often encounters situations with non-stationary environments and in these scenarios, RL methods yield sub-optimal decisions. In this paper, we thus consider the problem of developing RL methods that obtain optimal decisions in a non-stationary environment. The goal of this problem is to maximize the long-term discounted reward achieved when the underlying model of the environment changes over time. To achieve this, we first adapt a change point algorithm to detect change in the statistics of the environment and then develop an RL algorithm that maximizes the long-run reward accrued. We illustrate that our change point method detects change in the model of the environment effectively and thus facilitates the RL algorithm in maximizing the long-run reward. We further validate the effectiveness of the proposed solution on non-stationary random Markov decision processes, a sensor energy management problem and a traffic signal control problem.

cs.LG↗

arXiv2020

Generalized Speedy Q-learning

In this paper, we derive a generalization of the Speedy Q-learning (SQL) algorithm that was proposed in the Reinforcement Learning (RL) literature to handle slow convergence of Watkins' Q-learning. In most RL algorithms such as Q-learning, the Bellman equation and the Bellman operator play an important role. It is possible to generalize the Bellman operator using the technique of successive relaxation. We use the generalized Bellman operator to derive a simple and efficient family of algorithms called Generalized Speedy Q-learning (GSQL-w) and analyze its finite time performance. We show that GSQL-w has an improved finite time performance bound compared to SQL for the case when the relaxation parameter w is greater than 1. This improvement is a consequence of the contraction factor of the generalized Bellman operator being less than that of the standard Bellman operator. Numerical experiments are provided to demonstrate the empirical performance of the GSQL-w algorithm.

cs.LG↗

arXiv2019

Gait Library Synthesis for Quadruped Robots via Augmented Random Search

In this paper, with a view toward fast deployment of learned locomotion gaits in low-cost hardware, we generate a library of walking trajectories, namely, forward trot, backward trot, side-step, and turn in our custom-built quadruped robot, Stoch 2, using reinforcement learning. There are existing approaches that determine optimal policies for each time step, whereas we determine an optimal policy, in the form of end-foot trajectories, for each half walking step i.e., swing phase and stance phase. The way-points for the foot trajectories are obtained from a linear policy, i.e., a linear function of the states of the robot, and cubic splines are used to interpolate between these points. Augmented Random Search, a model-free and gradient-free learning algorithm is used to learn the policy in simulation. This learned policy is then deployed on hardware, yielding a trajectory in every half walking step. Different locomotion patterns are learned in simulation by enforcing a preconfigured phase shift between the trajectories of different legs. The transition from one gait to another is achieved by using a low-pass filter for the phase, and the sim-to-real transfer is improved by a linear transformation of the states obtained through regression.

cs.RO↗

arXiv2019

Hierarchical Average Reward Policy Gradient Algorithms

Option-critic learning is a general-purpose reinforcement learning (RL) framework that aims to address the issue of long term credit assignment by leveraging temporal abstractions. However, when dealing with extended timescales, discounting future rewards can lead to incorrect credit assignments. In this work, we address this issue by extending the hierarchical option-critic policy gradient theorem for the average reward criterion. Our proposed framework aims to maximize the long-term reward obtained in the steady-state of the Markov chain defined by the agent's policy. Furthermore, we use an ordinary differential equation based approach for our convergence analysis and prove that the parameters of the intra-option policies, termination functions, and value functions, converge to their corresponding optimal values, with probability one. Finally, we illustrate the competitive advantage of learning options, in the average reward setting, on a grid-world environment with sparse rewards.

cs.LG↗

arXiv2019

A Convergent Off-Policy Temporal Difference Algorithm

Learning the value function of a given policy (target policy) from the data samples obtained from a different policy (behavior policy) is an important problem in Reinforcement Learning (RL). This problem is studied under the setting of off-policy prediction. Temporal Difference (TD) learning algorithms are a popular class of algorithms for solving the prediction problem. TD algorithms with linear function approximation are shown to be convergent when the samples are generated from the target policy (known as on-policy prediction). However, it has been well established in the literature that off-policy TD algorithms under linear function approximation diverge. In this work, we propose a convergent on-line off-policy TD algorithm under linear function approximation. The main idea is to penalize the updates of the algorithm in a way as to ensure convergence of the iterates. We provide a convergence analysis of our algorithm. Through numerical evaluations, we further demonstrate the effectiveness of our algorithm.

cs.LG↗

arXiv2019

On the function approximation error for risk-sensitive reinforcement learning

In this paper we obtain several informative error bounds on function approximation for the policy evaluation algorithm proposed by Basu et al. when the aim is to find the risk-sensitive cost represented using exponential utility. The main idea is to use classical Bapat's inequality and to use Perron-Frobenius eigenvectors (exists if we assume irreducible Markov chain) to get the new bounds. The novelty of our approach is that we use the irreduciblity of Markov chain to get the new bounds whereas the earlier work by Basu et al. used spectral variation bound which is true for any matrix. We also give examples where all our bounds achieve the "actual error" whereas the earlier bound given by Basu et al. is much weaker in comparison. We show that this happens due to the absence of difference term in the earlier bound which is always present in all our bounds when the state space is large. Additionally, we discuss how all our bounds compare with each other. As a corollary of our main result we provide a bound between largest eigenvalues of two irreducibile matrices in terms of the matrix entries.

cs.LG↗