New algorithms of the Q-learning type

We propose two algorithms for Q-learning that use the two-timescale stochastic approximation methodology. The first of these updates Q-values of all feasible state–action pairs at each instant while the second updates Q-values of states with actions chosen according to the ‘current’ randomized policy updates. A proof of convergence of the algorithms is shown. Finally, numerical experiments using the proposed algorithms on an application of routing in communication networks are presented on a few different settings.

Two-timescale Q-learning Algorithms with an Application to Routing in Networks

We propose two variants of the Q-learning algorithm that (both) use two timescales. One of these updates Q-values of all feasible state-action pairs at each instant while the other updates Q-values of states with actions chosen according to the ‘current ’ randomized policy updates. A sketch of convergence of the algorithms is shown. Finally, numerical experiments using the proposed algorithms for routing on different network topologies are presented and performance comparisons with the regular Q-learning algorithm are shown.

A novel Q-learning algorithm with function approximation for constrained Markov decision processes

We present a novel multi-timescale Q-learning algorithm for average cost control in a Markov decision process subject to multiple inequality constraints. We formulate a relaxed version of this problem through the Lagrange multiplier method. Our algorithm is different from Q-learning in that it updates two parameters - a Q-value parameter and a policy parameter. The Q-value parameter is updated on a slower time scale as compared to the policy parameter. Whereas Q-learning with function approximation can diverge in some cases, our algorithm is seen to be convergent as a result of the aforementioned timescale separation. We show the results of experiments on a problem of constrained routing in a multistage queueing network. Our algorithm is seen to exhibit good performance and the various inequality constraints are seen to be satisfied upon convergence of the algorithm.

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. We study the problem of scheduling the sleep times of the individual sensors, where the objective is 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 stateaction spaces, in a manner similar to Fuemmeler and Veeravalli (IEEE Trans Signal Process 56(5), 2091-2101, 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. Feature-based representations and function approximation is necessary 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 estimate on the faster timescale, while the Q-value parameter (arising from a linear function approximation architecture for the Q-values) is updated in an on-policy temporal difference 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 and this is useful in settings where the latter is not known. Our simulation results on a synthetic 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.

Learning Multirobot Hose Transportation and Deployment by Distributed Round-Robin Q-Learning

Multi-Agent Reinforcement Learning (MARL) algorithms face two main difficulties: the curse of dimensionality, and environment non-stationarity due to the independent learning processes carried out by the agents concurrently. In this paper we formalize and prove the convergence of a Distributed Round Robin Q-learning (D-RR-QL) algorithm for cooperative systems. The computational complexity of this algorithm increases linearly with the number of agents. Moreover, it eliminates environment non sta tionarity by carrying a round-robin scheduling of the action selection and execution. That this learning scheme allows the implementation of Modular State-Action Vetoes (MSAV) in cooperative multi-agent systems, which speeds up learning convergence in over-constrained systems by vetoing state-action pairs which lead to undesired termination states (UTS) in the relevant state-action subspace. Each agent's local state-action value function learning is an independent process, including the MSAV policies. Coordination of locally optimal policies to obtain the global optimal joint policy is achieved by a greedy selection procedure using message passing. We show that D-RR-QL improves over state-of-the-art approaches, such as Distributed Q-Learning, Team Q-Learning and Coordinated Reinforcement Learning in a paradigmatic Linked Multi-Component Robotic System (L-MCRS) control problem: the hose transportation task. L-MCRS are over-constrained systems with many UTS induced by the interaction of the passive linking element and the active mobile robots.

Intelligent decision making in electricity markets: simulated annealing Q-Learning

Electricity markets are complex environments, involving a large number of different entities, playing in a dynamic scene to obtain the best advantages and profits. MASCEM is a multi-agent electricity market simulator to model market players and simulate their operation in the market. Market players are entities with specific characteristics and objectives, making their decisions and interacting with other players. MASCEM is integrated with ALBidS, a system that provides several dynamic strategies for agents’ behavior. This paper presents a method that aims at enhancing ALBidS competence in endowing market players with adequate strategic bidding capabilities, allowing them to obtain the higher possible gains out of the market. This method uses a reinforcement learning algorithm to learn from experience how to choose the best from a set of possible actions. These actions are defined accordingly to the most probable points of bidding success. With the purpose of accelerating the convergence process, a simulated annealing based algorithm is included.

Distributed Q-learning controller for a multi-intersection traffic network

This paper proposes a Q-learning based controller for a network of multi intersections. According to the increasing amount of traffic congestion in modern cities, using an efficient control system is demanding. The proposed controller designed to adjust the green time for traffic signals by the aim of reducing the vehicles’ travel delay time in a multi-intersection network. The designed system is a distributed traffic timing control model, applies individual controller for each intersection. Each controller adjusts its own intersection’s congestion while attempt to reduce the travel delay time in whole traffic network. The results of experiments indicate the satisfied efficiency of the developed distributed Q-learning controller.

Algoritmo Q-learning como estratégia de exploração e/ou explotação para metaheurísticas GRASP e algoritmo genético

Techniques of optimization known as metaheuristics have achieved success in the resolution of many problems classified as NP-Hard. These methods use non deterministic approaches that reach very good solutions which, however, don t guarantee the determination of the global optimum. Beyond the inherent difficulties related to the complexity that characterizes the optimization problems, the metaheuristics still face the dilemma of xploration/exploitation, which consists of choosing between a greedy search and a wider exploration of the solution space. A way to guide such algorithms during the searching of better solutions is supplying them with more knowledge of the problem through the use of a intelligent agent, able to recognize promising regions and also identify when they should diversify the direction of the search. This way, this work proposes the use of Reinforcement Learning technique - Q-learning Algorithm - as exploration/exploitation strategy for the metaheuristics GRASP (Greedy Randomized Adaptive Search Procedure) and Genetic Algorithm. The GRASP metaheuristic uses Q-learning instead of the traditional greedy-random algorithm in the construction phase. This replacement has the purpose of improving the quality of the initial solutions that are used in the local search phase of the GRASP, and also provides for the metaheuristic an adaptive memory mechanism that allows the reuse of good previous decisions and also avoids the repetition of bad decisions. In the Genetic Algorithm, the Q-learning algorithm was used to generate an initial population of high fitness, and after a determined number of generations, where the rate of diversity of the population is less than a certain limit L, it also was applied to supply one of the parents to be used in the genetic crossover operator. Another significant change in the hybrid genetic algorithm is the proposal of a mutually interactive cooperation process between the genetic operators and the Q-learning algorithm. In this interactive/cooperative process, the Q-learning algorithm receives an additional update in the matrix of Q-values based on the current best solution of the Genetic Algorithm. The computational experiments presented in this thesis compares the results obtained with the implementation of traditional versions of GRASP metaheuristic and Genetic Algorithm, with those obtained using the proposed hybrid methods. Both algorithms had been applied successfully to the symmetrical Traveling Salesman Problem, which was modeled as a Markov decision process

Learning dynamic prices in multiseller electronic retail markets with price sensitive customers, stochastic demands, and inventory replenishments

In this paper, we use reinforcement learning (RL) as a tool to study price dynamics in an electronic retail market consisting of two competing sellers, and price sensitive and lead time sensitive customers. Sellers, offering identical products, compete on price to satisfy stochastically arriving demands (customers), and follow standard inventory control and replenishment policies to manage their inventories. In such a generalized setting, RL techniques have not previously been applied. We consider two representative cases: 1) no information case, were none of the sellers has any information about customer queue levels, inventory levels, or prices at the competitors; and 2) partial information case, where every seller has information about the customer queue levels and inventory levels of the competitors. Sellers employ automated pricing agents, or pricebots, which use RL-based pricing algorithms to reset the prices at random intervals based on factors such as number of back orders, inventory levels, and replenishment lead times, with the objective of maximizing discounted cumulative profit. In the no information case, we show that a seller who uses Q-learning outperforms a seller who uses derivative following (DF). In the partial information case, we model the problem as a Markovian game and use actor-critic based RL to learn dynamic prices. We believe our approach to solving these problems is a new and promising way of setting dynamic prices in multiseller environments with stochastic demands, price sensitive customers, and inventory replenishments.

Reinforcement learning with average cost for adaptive control of traffic lights at intersections

We propose for the first time two reinforcement learning algorithms with function approximation for average cost adaptive control of traffic lights. One of these algorithms is a version of Q-learning with function approximation while the other is a policy gradient actor-critic algorithm that incorporates multi-timescale stochastic approximation. We show performance comparisons on various network settings of these algorithms with a range of fixed timing algorithms, as well as a Q-learning algorithm with full state representation that we also implement. We observe that whereas (as expected) on a two-junction corridor, the full state representation algorithm shows the best results, this algorithm is not implementable on larger road networks. The algorithm PG-AC-TLC that we propose is seen to show the best overall performance.

Reinforcement learning applications in dynamic pricing of retail markets

In this paper, we investigate the use of reinforcement learning (RL) techniques to the problem of determining dynamic prices in an electronic retail market. As representative models, we consider a single seller market and a two seller market, and formulate the dynamic pricing problem in a setting that easily generalizes to markets with more than two sellers. We first formulate the single seller dynamic pricing problem in the RL framework and solve the problem using the Q-learning algorithm through simulation. Next we model the two seller dynamic pricing problem as a Markovian game and formulate the problem in the RL framework. We solve this problem using actor-critic algorithms through simulation. We believe our approach to solving these problems is a promising way of setting dynamic prices in multi-agent environments. We illustrate the methodology with two illustrative examples of typical retail markets.

A neural network based automatic generation control design through reinforcement learning

This paper presents the design and implementation of a learning controller for the Automatic Generation Control (AGC) in power systems based on a reinforcement learning (RL) framework. In contrast to the recent RL scheme for AGC proposed by us, the present method permits handling of power system variables such as Area Control Error (ACE) and deviations from scheduled frequency and tie-line flows as continuous variables. (In the earlier scheme, these variables have to be quantized into finitely many levels). The optimal control law is arrived at in the RL framework by making use of Q-learning strategy. Since the state variables are continuous, we propose the use of Radial Basis Function (RBF) neural networks to compute the Q-values for a given input state. Since, in this application we cannot provide training data appropriate for the standard supervised learning framework, a reinforcement learning algorithm is employed to train the RBF network. We also employ a novel exploration strategy, based on a Learning Automata algorithm,for generating training samples during Q-learning. The proposed scheme, in addition to being simple to implement, inherits all the attractive features of an RL scheme such as model independent design, flexibility in control objective specification, robustness etc. Two implementations of the proposed approach are presented. Through simulation studies the attractiveness of this approach is demonstrated.