arXiv subjects

Amrit Singh Bedi

Publications and source records attributed to Amrit Singh Bedi.

At least 91 records · Page 5Linked to original sources

arXiv2022

DC-MRTA: Decentralized Multi-Robot Task Allocation and Navigation in Complex Environments

We present a novel reinforcement learning (RL) based task allocation and decentralized navigation algorithm for mobile robots in warehouse environments. Our approach is designed for scenarios in which multiple robots are used to perform various pick up and delivery tasks. We consider the problem of joint decentralized task allocation and navigation and present a two level approach to solve it. At the higher level, we solve the task allocation by formulating it in terms of Markov Decision Processes and choosing the appropriate rewards to minimize the Total Travel Delay (TTD). At the lower level, we use a decentralized navigation scheme based on ORCA that enables each robot to perform these tasks in an independent manner, and avoid collisions with other robots and dynamic obstacles. We combine these lower and upper levels by defining rewards for the higher level as the feedback from the lower level navigation algorithm. We perform extensive evaluation in complex warehouse layouts with large number of agents and highlight the benefits over state-of-the-art algorithms based on myopic pickup distance minimization and regret-based task selection. We observe improvement up to 14% in terms of task completion time and up-to 40% improvement in terms of computing collision-free trajectories for the robots.

cs.RO↗

arXiv2022

Distributed Riemannian Optimization with Lazy Communication for Collaborative Geometric Estimation

We present the first distributed optimization algorithm with lazy communication for collaborative geometric estimation, the backbone of modern collaborative simultaneous localization and mapping (SLAM) and structure-from-motion (SfM) applications. Our method allows agents to cooperatively reconstruct a shared geometric model on a central server by fusing individual observations, but without the need to transmit potentially sensitive information about the agents themselves (such as their locations). Furthermore, to alleviate the burden of communication during iterative optimization, we design a set of communication triggering conditions that enable agents to selectively upload a targeted subset of local information that is useful to global optimization. Our approach thus achieves significant communication reduction with minimal impact on optimization performance. As our main theoretical contribution, we prove that our method converges to first-order critical points with a global sublinear convergence rate. Numerical evaluations on bundle adjustment problems from collaborative SLAM and SfM datasets show that our method performs competitively against existing distributed techniques, while achieving up to 78% total communication reduction.

cs.RO↗

arXiv2022

Achieving Zero Constraint Violation for Constrained Reinforcement Learning via Primal-Dual Approach

Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety constraints. The problem is mathematically formulated as constrained Markov decision process (CMDP). In the literature, various algorithms are available to solve CMDP problems in a model-free manner to achieve $ε$-optimal cumulative reward with $ε$ feasible policies. An $ε$-feasible policy implies that it suffers from constraint violation. An important question here is whether we can achieve $ε$-optimal cumulative reward with zero constraint violations or not. To achieve that, we advocate the use of randomized primal-dual approach to solve the CMDP problems and propose a conservative stochastic primal-dual algorithm (CSPDA) which is shown to exhibit $\tilde{\mathcal{O}}\left(1/ε^2\right)$ sample complexity to achieve $ε$-optimal cumulative reward with zero constraint violations. In the prior works, the best available sample complexity for the $ε$-optimal policy with zero constraint violation is $\tilde{\mathcal{O}}\left(1/ε^5\right)$. Hence, the proposed algorithm provides a significant improvement as compared to the state of the art.

cs.LG↗

arXiv2022

Dealing with Sparse Rewards in Continuous Control Robotics via Heavy-Tailed Policies

In this paper, we present a novel Heavy-Tailed Stochastic Policy Gradient (HT-PSG) algorithm to deal with the challenges of sparse rewards in continuous control problems. Sparse reward is common in continuous control robotics tasks such as manipulation and navigation, and makes the learning problem hard due to non-trivial estimation of value functions over the state space. This demands either reward shaping or expert demonstrations for the sparse reward environment. However, obtaining high-quality demonstrations is quite expensive and sometimes even impossible. We propose a heavy-tailed policy parametrization along with a modified momentum-based policy gradient tracking scheme (HT-SPG) to induce a stable exploratory behavior to the algorithm. The proposed algorithm does not require access to expert demonstrations. We test the performance of HT-SPG on various benchmark tasks of continuous control with sparse rewards such as 1D Mario, Pathological Mountain Car, Sparse Pendulum in OpenAI Gym, and Sparse MuJoCo environments (Hopper-v2). We show consistent performance improvement across all tasks in terms of high average cumulative reward. HT-SPG also demonstrates improved convergence speed with minimum samples, thereby emphasizing the sample efficiency of our proposed algorithm.

cs.LG↗

arXiv2022

Projection-Free Algorithm for Stochastic Bi-level Optimization

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic $\textbf{Bi}$-level $\textbf{F}$rank-$\textbf{W}$olfe ($\textbf{SBFW}$) algorithm can be applied to streaming settings and does not make use of large batches or checkpoints. The sample complexity of SBFW is shown to be $\mathcal{O}(ε^{-3})$ for convex objectives and $\mathcal{O}(ε^{-4})$ for non-convex objectives. Improved rates are derived for the stochastic compositional problem, which is a special case of the bi-level problem, and entails minimizing the composition of two expected-value functions. The proposed $\textbf{S}$tochastic $\textbf{C}$ompositional $\textbf{F}$rank-$\textbf{W}$olfe ($\textbf{SCFW}$) is shown to achieve a sample complexity of $\mathcal{O}(ε^{-2})$ for convex objectives and $\mathcal{O}(ε^{-3})$ for non-convex objectives, at par with the state-of-the-art sample complexities for projection-free algorithms solving single-level problems. We demonstrate the advantage of the proposed methods by solving the problem of matrix completion with denoising and the problem of policy value evaluation in reinforcement learning.

math.OC↗

arXiv2022

Regret and Belief Complexity Trade-off in Gaussian Process Bandits via Information Thresholding

Bayesian optimization is a framework for global search via maximum a posteriori updates rather than simulated annealing, and has gained prominence for decision-making under uncertainty. In this work, we cast Bayesian optimization as a multi-armed bandit problem, where the payoff function is sampled from a Gaussian process (GP). Further, we focus on action selections via upper confidence bound (UCB) or expected improvement (EI) due to their prevalent use in practice. Prior works using GPs for bandits cannot allow the iteration horizon $T$ to be large, as the complexity of computing the posterior parameters scales cubically with the number of past observations. To circumvent this computational burden, we propose a simple statistical test: only incorporate an action into the GP posterior when its conditional entropy exceeds an $ε$ threshold. Doing so permits us to precisely characterize the trade-off between regret bounds of GP bandit algorithms and complexity of the posterior distributions depending on the compression parameter $ε$ for both discrete and continuous action sets. To best of our knowledge, this is the first result which allows us to obtain sublinear regret bounds while still maintaining sublinear growth rate of the complexity of the posterior which is linear in the existing literature. Moreover, a provably finite bound on the complexity could be achieved but the algorithm would result in $ε$-regret which means $\textbf{Reg}_T/T \rightarrow \mathcal{O}(ε)$ as $T\rightarrow \infty$. Experimentally, we observe state of the art accuracy and complexity trade-offs for GP bandit algorithms applied to global optimization, suggesting the merits of compressed GPs in bandit settings.

cs.LG↗

arXiv2022

On the Hidden Biases of Policy Mirror Ascent in Continuous Action Spaces

We focus on parameterized policy search for reinforcement learning over continuous action spaces. Typically, one assumes the score function associated with a policy is bounded, which fails to hold even for Gaussian policies. To properly address this issue, one must introduce an exploration tolerance parameter to quantify the region in which it is bounded. Doing so incurs a persistent bias that appears in the attenuation rate of the expected policy gradient norm, which is inversely proportional to the radius of the action space. To mitigate this hidden bias, heavy-tailed policy parameterizations may be used, which exhibit a bounded score function, but doing so can cause instability in algorithmic updates. To address these issues, in this work, we study the convergence of policy gradient algorithms under heavy-tailed parameterizations, which we propose to stabilize with a combination of mirror ascent-type updates and gradient tracking. Our main theoretical contribution is the establishment that this scheme converges with constant step and batch sizes, whereas prior works require these parameters to respectively shrink to null or grow to infinity. Experimentally, this scheme under a heavy-tailed policy parameterization yields improved reward accumulation across a variety of settings as compared with standard benchmarks.

cs.LG↗

arXiv2021

Convergence Rates of Average-Reward Multi-agent Reinforcement Learning via Randomized Linear Programming

In tabular multi-agent reinforcement learning with average-cost criterion, a team of agents sequentially interacts with the environment and observes local incentives. We focus on the case that the global reward is a sum of local rewards, the joint policy factorizes into agents' marginals, and full state observability. To date, few global optimality guarantees exist even for this simple setting, as most results yield convergence to stationarity for parameterized policies in large/possibly continuous spaces. To solidify the foundations of MARL, we build upon linear programming (LP) reformulations, for which stochastic primal-dual methods yields a model-free approach to achieve \emph{optimal sample complexity} in the centralized case. We develop multi-agent extensions, whereby agents solve their local saddle point problems and then perform local weighted averaging. We establish that the sample complexity to obtain near-globally optimal solutions matches tight dependencies on the cardinality of the state and action spaces, and exhibits classical scalings with respect to the network in accordance with multi-agent optimization. Experiments corroborate these results in practice.

math.OC↗

arXiv2021

Wasserstein-Splitting Gaussian Process Regression for Heterogeneous Online Bayesian Inference

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior distributions. Over time, then, this yields an ensemble of sparse GPs which may be updated incrementally, and adapts to locality, heterogeneity, and non-stationarity in training data.

stat.ML↗

arXiv2021

MARL with General Utilities via Decentralized Shadow Reward Actor-Critic

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $ε$-stationarity in $\mathcal{O}(1/ε^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/ε^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.

stat.ML↗

arXiv2021

Adaptive Kernel Learning in Heterogeneous Networks

We consider learning in decentralized heterogeneous networks: agents seek to minimize a convex functional that aggregates data across the network, while only having access to their local data streams. We focus on the case where agents seek to estimate a regression \emph{function} that belongs to a reproducing kernel Hilbert space (RKHS). To incentivize coordination while respecting network heterogeneity, we impose nonlinear proximity constraints. To solve the constrained stochastic program, we propose applying a functional variant of stochastic primal-dual (Arrow-Hurwicz) method which yields a decentralized algorithm. To handle the fact that agents' functions have complexity proportional to time (owing to the RKHS parameterization), we project the primal iterates onto subspaces greedily constructed from kernel evaluations of agents' local observations. The resulting scheme, dubbed Heterogeneous Adaptive Learning with Kernels (HALK), when used with constant step-sizes, yields $\mathcal{O}(\sqrt{T})$ attenuation in sub-optimality and exactly satisfies the constraints in the long run, which improves upon the state of the art rates for vector-valued problems.

math.OC↗

arXiv2021

Conservative Stochastic Optimization with Expectation Constraints

This paper considers stochastic convex optimization problems where the objective and constraint functions involve expectations with respect to the data indices or environmental variables, in addition to deterministic convex constraints on the domain of the variables. Although the setting is generic and arises in different machine learning applications, online and efficient approaches for solving such problems have not been widely studied. Since the underlying data distribution is unknown a priori, a closed-form solution is generally not available, and classical deterministic optimization paradigms are not applicable. State-of-the-art approaches, such as those using the saddle point framework, can ensure that the optimality gap as well as the constraint violation decay as $Ø\left(T^{-\frac{1}{2}}\right)$ where $T$ is the number of stochastic gradients. The domain constraints are assumed simple and handled via projection at every iteration. In this work, we propose a novel conservative stochastic optimization algorithm (CSOA) that achieves zero constraint violation and $Ø\left(T^{-\frac{1}{2}}\right)$ optimality gap. Further, the projection operation (for scenarios when calculating projection is expensive) in the proposed algorithm can be avoided by considering the conditional gradient or Frank-Wolfe (FW) variant of the algorithm. The state-of-the-art stochastic FW variants achieve an optimality gap of $Ø\left(T^{-\frac{1}{3}}\right)$ after $T$ iterations, though these algorithms have not been applied to problems with functional expectation constraints. In this work, we propose the FW-CSOA algorithm that is not only projection-free but also achieves zero constraint violation with $Ø\left(T^{-\frac{1}{4}}\right)$ decay of the optimality gap. The efficacy of the proposed algorithms is tested on two relevant problems: fair classification and structured matrix completion.

math.OC↗

arXiv2021

Nearly Consistent Finite Particle Estimates in Streaming Importance Sampling

In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC) sampling is usually required. {Importance sampling is a standard MC tool that approximates this unavailable distribution with a set of weighted samples.} This procedure is asymptotically consistent as the number of MC samples (particles) go to infinity. However, retaining infinitely many particles is intractable. Thus, we propose a way to only keep a \emph{finite representative subset} of particles and their augmented importance weights that is \emph{nearly consistent}. To do so in {an online manner}, we (1) embed the posterior density estimate in a reproducing kernel Hilbert space (RKHS) through its kernel mean embedding; and (2) sequentially project this RKHS element onto a lower-dimensional subspace in RKHS using the maximum mean discrepancy, an integral probability metric. Theoretically, we establish that this scheme results in a bias determined by a compression parameter, which yields a tunable tradeoff between consistency and memory. In experiments, we observe the compressed estimates achieve comparable performance to the dense ones with substantial reductions in representational complexity.

math.ST↗

arXiv2020

Nonparametric Compositional Stochastic Optimization for Risk-Sensitive Kernel Learning

In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not vector-valued but instead belongs to a reproducing Kernel Hilbert Space (RKHS), motivated by risk-aware formulations of supervised learning and Markov Decision Processes defined over continuous spaces. We develop the first memory-efficient stochastic algorithm for this setting, which we call Compositional Online Learning with Kernels (COLK). COLK, at its core a two-time-scale stochastic approximation method, addresses the fact that (i) compositions of expected value problems cannot be addressed by classical stochastic gradient due to the presence of the inner expectation; and (ii) the RKHS-induced parameterization has complexity which is proportional to the iteration index which is mitigated through greedily constructed subspace projections. We establish almost sure convergence of COLK with attenuating step-sizes, and linear convergence in mean to a neighborhood with constant step-sizes, as well as the fact that its complexity is at-worst finite. The experiments with robust formulations of supervised learning demonstrate that COLK reliably converges, attains consistent performance across training runs, and thus overcomes overfitting.

math.OC↗

arXiv2020

Variational Policy Gradient Method for Reinforcement Learning with General Utilities

In recent years, reinforcement learning (RL) systems with general goals beyond a cumulative sum of rewards have gained traction, such as in constrained problems, exploration, and acting upon prior experiences. In this paper, we consider policy optimization in Markov Decision Problems, where the objective is a general concave utility function of the state-action occupancy measure, which subsumes several of the aforementioned examples as special cases. Such generality invalidates the Bellman equation. As this means that dynamic programming no longer works, we focus on direct policy search. Analogously to the Policy Gradient Theorem \cite{sutton2000policy} available for RL with cumulative rewards, we derive a new Variational Policy Gradient Theorem for RL with general utilities, which establishes that the parametrized policy gradient may be obtained as the solution of a stochastic saddle point problem involving the Fenchel dual of the utility function. We develop a variational Monte Carlo gradient estimation algorithm to compute the policy gradient based on sample paths. We prove that the variational policy gradient scheme converges globally to the optimal policy for the general objective, though the optimization problem is nonconvex. We also establish its rate of convergence of the order $O(1/t)$ by exploiting the hidden convexity of the problem, and proves that it converges exponentially when the problem admits hidden strong convexity. Our analysis applies to the standard RL problem with cumulative rewards as a special case, in which case our result improves the available convergence rate.

cs.LG↗

arXiv2020

Cautious Reinforcement Learning via Distributional Risk in the Dual Domain

We study the estimation of risk-sensitive policies in reinforcement learning problems defined by a Markov Decision Process (MDPs) whose state and action spaces are countably finite. Prior efforts are predominately afflicted by computational challenges associated with the fact that risk-sensitive MDPs are time-inconsistent. To ameliorate this issue, we propose a new definition of risk, which we call caution, as a penalty function added to the dual objective of the linear programming (LP) formulation of reinforcement learning. The caution measures the distributional risk of a policy, which is a function of the policy's long-term state occupancy distribution. To solve this problem in an online model-free manner, we propose a stochastic variant of primal-dual method that uses Kullback-Lieber (KL) divergence as its proximal term. We establish that the number of iterations/samples required to attain approximately optimal solutions of this scheme matches tight dependencies on the cardinality of the state and action spaces, but differs in its dependence on the infinity norm of the gradient of the risk measure. Experiments demonstrate the merits of this approach for improving the reliability of reward accumulation without additional computational burdens.

stat.ML↗

arXiv2020

Optimally Compressed Nonparametric Online Learning

Batch training of machine learning models based on neural networks is now well established, whereas to date streaming methods are largely based on linear models. To go beyond linear in the online setting, nonparametric methods are of interest due to their universality and ability to stably incorporate new information via convexity or Bayes' Rule. Unfortunately, when used online, nonparametric methods suffer a "curse of dimensionality" which precludes their use: their complexity scales at least with the time index. We survey online compression tools which bring their memory under control and attain approximate convergence. The asymptotic bias depends on a compression parameter that trades off memory and accuracy. Further, the applications to robotics, communications, economics, and power are discussed, as well as extensions to multi-agent systems.

eess.SP↗

arXiv2020

Online Trajectory Optimization Using Inexact Gradient Feedback for Time-Varying Environments

This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel version of the online gradient ascent algorithm for such problems. Moreover, the gradient feedback is noisy and allows us to use the proposed algorithm for a range of practical applications where it is difficult to acquire the true gradient. In contrast to the most available literature, we present the offline sublinear regret of the proposed algorithm up to the path length variations of the optimal offline solution, the cumulative gradient, and the error in the gradient variations. Furthermore, we establish a lower bound on the offline dynamic regret, which defines the optimality of any trajectory. To show the efficacy of the proposed algorithm, we consider two practical problems of interest. First, we consider a device to device (D2D) communications setting, and the goal is to design a user trajectory while maximizing its connectivity to the internet. The second problem is associated with the online planning of energy-efficient trajectories for unmanned surface vehicles (USV) under strong disturbances in ocean environments with both static and dynamic goal locations. The detailed simulation results demonstrate the significance of the proposed algorithm on synthetic and real data sets. Video on the real-world datasets can be found at {https://www.youtube.com/watch?v=FcRqqWtpf\_0}

math.OC↗