arXiv subjects

Prashanth L. A.

Publications and source records attributed to Prashanth L. A..

26 records · Page 2Linked to original sources

arXiv2018

Concentration bounds for empirical conditional value-at-risk: The unbounded case

In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional Value-at-Risk (CVaR) is a popular risk measure for modeling the aforementioned objective. We consider the problem of estimating CVaR from i.i.d. samples of an unbounded random variable, which is either sub-Gaussian or sub-exponential. We derive a novel one-sided concentration bound for a natural sample-based CVaR estimator in this setting. Our bound relies on a concentration result for a quantile-based estimator for Value-at-Risk (VaR), which may be of independent interest.

cs.LG↗

arXiv2016

Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and Control

Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent risk measures. We bring this idea to a risk-sensitive reinforcement learning (RL) setting and design algorithms for both estimation and control. The RL setting presents two particular challenges when CPT is applied: estimating the CPT objective requires estimations of the entire distribution of the value function and finding a randomized optimal policy. The estimation scheme that we propose uses the empirical distribution to estimate the CPT-value of a random variable. We then use this scheme in the inner loop of a CPT-value optimization procedure that is based on the well-known simulation optimization idea of simultaneous perturbation stochastic approximation (SPSA). We provide theoretical convergence guarantees for all the proposed algorithms and also illustrate the usefulness of CPT-based criteria in a traffic signal control application.

cs.LG↗

arXiv2015

Adaptive system optimization using random directions stochastic approximation

We present novel algorithms for simulation optimization using random directions stochastic approximation (RDSA). These include first-order (gradient) as well as second-order (Newton) schemes. We incorporate both continuous-valued as well as discrete-valued perturbations into both our algorithms. The former are chosen to be independent and identically distributed (i.i.d.) symmetric, uniformly distributed random variables (r.v.), while the latter are i.i.d., asymmetric, Bernoulli r.v.s. Our Newton algorithm, with a novel Hessian estimation scheme, requires N-dimensional perturbations and three loss measurements per iteration, whereas the simultaneous perturbation Newton search algorithm of [1] requires 2N-dimensional perturbations and four loss measurements per iteration. We prove the unbiasedness of both gradient and Hessian estimates and asymptotic (strong) convergence for both first-order and second-order schemes. We also provide asymptotic normality results, which in particular establish that the asymmetric Bernoulli variant of Newton RDSA method is better than 2SPSA of [1]. Numerical experiments are used to validate the theoretical results.

math.OC↗

arXiv2015

A constrained optimization perspective on actor critic algorithms and application to network routing

We propose a novel actor-critic algorithm with guaranteed convergence to an optimal policy for a discounted reward Markov decision process. The actor incorporates a descent direction that is motivated by the solution of a certain non-linear optimization problem. We also discuss an extension to incorporate function approximation and demonstrate the practicality of our algorithms on a network routing application.

cs.LG↗

arXiv2015

Variance-Constrained Actor-Critic Algorithms for Discounted and Average Reward MDPs

In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For each of these criteria, we derive a formula for computing its gradient. We then devise actor-critic algorithms that operate on three timescales - a TD critic on the fastest timescale, a policy gradient (actor) on the intermediate timescale, and a dual ascent for Lagrange multipliers on the slowest timescale. In the discounted setting, we point out the difficulty in estimating the gradient of the variance of the return and incorporate simultaneous perturbation approaches to alleviate this. The average setting, on the other hand, allows for an actor update using compatible features to estimate the gradient of the variance. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in a traffic signal control application.

cs.LG↗

arXiv2014

Fast gradient descent for drifting least squares regression, with application to bandits

Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of classic regression solvers. We show that SGD schemes efficiently track the true solutions of the regression problems, even in the presence of a drift. This finding coupled with an $O(d)$ improvement in complexity, where $d$ is the dimension of the data, make them attractive for implementation in the big data settings. In the case when strong convexity in the regression problem is guaranteed, we provide bounds on the error both in expectation and high probability (the latter is often needed to provide theoretical guarantees for higher level algorithms), despite the drifting least squares solution. As an example of this case we prove that the regret performance of an SGD version of the PEGE linear bandit algorithm [Rusmevichientong and Tsitsiklis 2010] is worse that that of PEGE itself only by a factor of $O(\log^4 n)$. When strong convexity of the regression problem cannot be guaranteed, we investigate using an adaptive regularisation. We make an empirical study of an adaptively regularised, SGD version of LinUCB [Li et al. 2010] in a news article recommendation application, which uses the large scale news recommendation dataset from Yahoo! front page. These experiments show a large gain in computational complexity, with a consistently low tracking error and click-through-rate (CTR) performance that is $75\%$ close.

cs.LG↗

arXiv2014

Policy Gradients for CVaR-Constrained MDPs

We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four tools: stochastic approximation, mini batches, policy gradients and importance sampling. Both the algorithms incorporate a CVaR estimation procedure, along the lines of Bardou et al. [2009], which in turn is based on Rockafellar-Uryasev's representation for CVaR and utilize the likelihood ratio principle for estimating the gradient of the sum of one cost function (objective of the SSP) and the gradient of the CVaR of the sum of another cost function (in the constraint of SSP). The algorithms differ in the manner in which they approximate the CVaR estimates/necessary gradients - the first algorithm uses stochastic approximation, while the second employ mini-batches in the spirit of Monte Carlo methods. We establish asymptotic convergence of both the algorithms. Further, since estimating CVaR is related to rare-event simulation, we incorporate an importance sampling based variance reduction scheme into our proposed algorithms.

stat.ML↗

arXiv2014

Two Timescale Convergent Q-learning for Sleep--Scheduling in Wireless Sensor Networks

In this paper, we consider an intrusion detection application for Wireless Sensor Networks (WSNs). We study the problem of scheduling the sleep times of the individual sensors to maximize the network lifetime while keeping the tracking error to a minimum. We formulate this problem as a partially-observable Markov decision process (POMDP) with continuous state-action spaces, in a manner similar to (Fuemmeler and Veeravalli [2008]). However, unlike their formulation, we consider infinite horizon discounted and average cost objectives as performance criteria. For each criterion, we propose a convergent on-policy Q-learning algorithm that operates on two timescales, while employing function approximation to handle the curse of dimensionality associated with the underlying POMDP. Our proposed algorithm incorporates a policy gradient update using a one-simulation simultaneous perturbation stochastic approximation (SPSA) estimate on the faster timescale, while the Q-value parameter (arising from a linear function approximation for the Q-values) is updated in an on-policy temporal difference (TD) algorithm-like fashion on the slower timescale. The feature selection scheme employed in each of our algorithms manages the energy and tracking components in a manner that assists the search for the optimal sleep-scheduling policy. For the sake of comparison, in both discounted and average settings, we also develop a function approximation analogue of the Q-learning algorithm. This algorithm, unlike the two-timescale variant, does not possess theoretical convergence guarantees. Finally, we also adapt our algorithms to include a stochastic iterative estimation scheme for the intruder's mobility model. Our simulation results on a 2-dimensional network setting suggest that our algorithms result in better tracking accuracy at the cost of only a few additional sensors, in comparison to a recent prior work.

eess.SY↗