An actor-critic algorithm with function approximation for discounted cost constrained Markov decision processes

We develop in this article the first actor-critic reinforcement learning algorithm with function approximation for a problem of control under multiple inequality constraints. We consider the infinite horizon discounted cost framework in which both the objective and the constraint functions are suitable expected policy-dependent discounted sums of certain sample path functions. We apply the Lagrange multiplier method to handle the inequality constraints. Our algorithm makes use of multi-timescale stochastic approximation and incorporates a temporal difference (TD) critic and an actor that makes a gradient search in the space of policy parameters using efficient simultaneous perturbation stochastic approximation (SPSA) gradient estimates. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal policy. (C) 2010 Elsevier B.V. All rights reserved.

A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems

Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the �Single Network Adaptive Critic (SNAC)� is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.

Microstructure evolution during solidification of DRMMCs (discontinuously reinforced metal matrix composites): State of art

Distribution of particle reinforcements in cast composites is determined by the morphology of the solidification front. Interestingly, during solidification, the morphology of the interface is intrinsically affected by the presence of dispersed reinforcements. Thus the dispersoid distribution and length scale of matrix microstructure is a result of the interplay between these two. A proper combination of material and process parameters can be used to obtain composites with tailored microstructures. This requires the generation of a broad data base and optimization of the complete solidification process. The length scale of soldification microtructure has a large influence on the mechanical properties of the composites. This presentation addresses the concept of a particle distribution map which can help in predicting particle distribution under different solidification conditions Future research directions have also been indicated.

The actor-critic algorithm as multi-time-scale stochastic approximation

The actor-critic algorithm of Barto and others for simulation-based optimization of Markov decision processes is cast as a two time Scale stochastic approximation. Convergence analysis, approximation issues and an example are studied.

Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.

Incremental natural-gradient actor-critic algorithms

We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic rein- forcement learning methods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their com- patibility with function approximation methods, which are needed to handle large or infinite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further re- duce variance in some cases. Our results extend prior two-timescale convergence results for actor-critic methods by Konda and Tsitsiklis by using temporal differ- ence learning in the actor and by incorporating natural gradients, and they extend prior empirical studies of natural actor-critic methods by Peters, Vijayakumar and Schaal by providing the first convergence proofs and the first fully incremental algorithms.

An Actor-Critic Algorithm for Finite Horizon Markov Decision Processes

We develop a simulation based algorithm for finite horizon Markov decision processes with finite state and finite action space. Illustrative numerical experiments with the proposed algorithm are shown for problems in flow control of communication networks and capacity switching in semiconductor fabrication.

A Simultaneous Deterministic Perturbation Actor-Critic Algorithm with an Application to Optimal Mortgage Refinancing

We develop a simulation-based, two-timescale actor-critic algorithm for infinite horizon Markov decision processes with finite state and action spaces, with a discounted reward criterion. The algorithm is of the gradient ascent type and performs a search in the space of stationary randomized policies. The algorithm uses certain simultaneous deterministic perturbation stochastic approximation (SDPSA) gradient estimates for enhanced performance. We show an application of our algorithm on a problem of mortgage refinancing. Our algorithm obtains the optimal refinancing strategies in a computationally efficient manner

An Online Actor-Critic Algorithm with Function Approximation for Constrained Markov Decision Processes

We develop an online actor-critic reinforcement learning algorithm with function approximation for a problem of control under inequality constraints. We consider the long-run average cost Markov decision process (MDP) framework in which both the objective and the constraint functions are suitable policy-dependent long-run averages of certain sample path functions. The Lagrange multiplier method is used to handle the inequality constraints. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal solution. We also provide the results of numerical experiments on a problem of routing in a multi-stage queueing network with constraints on long-run average queue lengths. We observe that our algorithm exhibits good performance on this setting and converges to a feasible point.

Music and symbolic dynamics: the science behind an art

Music signals comprise of atomic notes drawn from a musical scale. The creation of musical sequences often involves splicing the notes in a constrained way resulting in aesthetically appealing patterns. We develop an approach for music signal representation based on symbolic dynamics by translating the lexicographic rules over a musical scale to constraints on a Markov chain. This source representation is useful for machine based music synthesis, in a way, similar to a musician producing original music. In order to mathematically quantify user listening experience, we study the correlation between the max-entropic rate of a musical scale and the subjective aesthetic component. We present our analysis with examples from the south Indian classical music system.

Automatic Tonic Identification in Indian Art Music: Approaches and Evaluation

The tonic is a fundamental concept in Indian art music. It is the base pitch, which an artist chooses in order to construct the melodies during a rg(a) rendition, and all accompanying instruments are tuned using the tonic pitch. Consequently, tonic identification is a fundamental task for most computational analyses of Indian art music, such as intonation analysis, melodic motif analysis and rg recognition. In this paper we review existing approaches for tonic identification in Indian art music and evaluate them on six diverse datasets for a thorough comparison and analysis. We study the performance of each method in different contexts such as the presence/absence of additional metadata, the quality of audio data, the duration of audio data, music tradition (Hindustani/Carnatic) and the gender of the singer (male/female). We show that the approaches that combine multi-pitch analysis with machine learning provide the best performance in most cases (90% identification accuracy on average), and are robust across the aforementioned contexts compared to the approaches based on expert knowledge. In addition, we also show that the performance of the latter can be improved when additional metadata is available to further constrain the problem. Finally, we present a detailed error analysis of each method, providing further insights into the advantages and limitations of the methods.

Progress in tuberculosis vaccine development and host-directed therapies-a state of the art review

Tuberculosis continues to kill 1.4 million people annually. During the past 5 years, an alarming increase in the number of patients with multidrug-resistant tuberculosis and extensively drug-resistant tuberculosis has been noted, particularly in eastern Europe, Asia, and southern Africa. Treatment outcomes with available treatment regimens for drug-resistant tuberculosis are poor. Although substantial progress in drug development for tuberculosis has been made, scientific progress towards development of interventions for prevention and improvement of drug treatment outcomes have lagged behind. Innovative interventions are therefore needed to combat the growing pandemic of multidrug-resistant and extensively drug-resistant tuberculosis. Novel adjunct treatments are needed to accomplish improved cure rates for multidrug-resistant and extensively drug-resistant tuberculosis. A novel, safe, widely applicable, and more effective vaccine against tuberculosis is also desperately sought to achieve disease control. The quest to develop a universally protective vaccine for tuberculosis continues. So far, research and development of tuberculosis vaccines has resulted in almost 20 candidates at different stages of the clinical trial pipeline. Host-directed therapies are now being developed to refocus the anti-Mycobacterium tuberculosis-directed immune responses towards the host; a strategy that could be especially beneficial for patients with multidrug-resistant tuberculosis or extensively drug-resistant tuberculosis. As we are running short of canonical tuberculosis drugs, more attention should be given to host-directed preventive and therapeutic intervention measures.