scholarly journals Conditions on Features for Temporal Difference-Like Methods to Converge

2019 ◽  
Author(s):  
Marcus Hutter ◽  
Samuel Yang-Zhao ◽  
Sultan Javed Majeed
Keyword(s):  
Reinforcement Learning ◽  
Function Approximation ◽  
Bellman Equation ◽  
Complete Characterization ◽  
Value Functions ◽  
Approximation Space ◽  
State Aggregation ◽  
Linear Function Approximation ◽  
The Value Function

The convergence of many reinforcement learning (RL) algorithms with linear function approximation has been investigated extensively but most proofs assume that these methods converge to a unique solution. In this paper, we provide a complete characterization of non-uniqueness issues for a large class of reinforcement learning algorithms, simultaneously unifying many counter-examples to convergence in a theoretical framework. We achieve this by proving a new condition on features that can determine whether the convergence assumptions are valid or non-uniqueness holds. We consider a general class of RL methods, which we call natural algorithms, whose solutions are characterized as the fixed point of a projected Bellman equation. Our main result proves that natural algorithms converge to the correct solution if and only if all the value functions in the approximation space satisfy a certain shape. This implies that natural algorithms are, in general, inherently prone to converge to the wrong solution for most feature choices even if the value function can be represented exactly. Given our results, we show that state aggregation-based features are a safe choice for natural algorithms and also provide a condition for finding convergent algorithms under other feature constructions.

scholarly journals Fixed-Horizon Temporal Difference Methods for Stable Reinforcement Learning

2020 ◽  
Vol 34 (04) ◽  
pp. 3741-3748
Author(s):  
Kristopher De Asis ◽  
Alan Chan ◽  
Silviu Pitis ◽  
Richard Sutton ◽  
Daniel Graves
Keyword(s):  
Reinforcement Learning ◽  
Function Approximation ◽  
Value Function ◽  
Temporal Difference ◽  
Value Functions ◽  
Difference Methods ◽  
Td Methods ◽  
The Stability ◽  
The Value Function ◽  
Temporal Difference Methods

We explore fixed-horizon temporal difference (TD) methods, reinforcement learning algorithms for a new kind of value function that predicts the sum of rewards over a fixed number of future time steps. To learn the value function for horizon h, these algorithms bootstrap from the value function for horizon h−1, or some shorter horizon. Because no value function bootstraps from itself, fixed-horizon methods are immune to the stability problems that plague other off-policy TD methods using function approximation (also known as “the deadly triad”). Although fixed-horizon methods require the storage of additional value functions, this gives the agent additional predictive power, while the added complexity can be substantially reduced via parallel updates, shared weights, and n-step bootstrapping. We show how to use fixed-horizon value functions to solve reinforcement learning problems competitively with methods such as Q-learning that learn conventional value functions. We also prove convergence of fixed-horizon temporal difference methods with linear and general function approximation. Taken together, our results establish fixed-horizon TD methods as a viable new way of avoiding the stability problems of the deadly triad.

FUZZY STATE AGGREGATION AND POLICY HILL CLIMBING FOR STOCHASTIC ENVIRONMENTS

2006 ◽  
Vol 06 (03) ◽  
pp. 413-428 ◽  
Author(s):  
DEAN C. WARDELL ◽  
GILBERT L. PETERSON
Keyword(s):  
Reinforcement Learning ◽  
Function Approximation ◽  
Hill Climbing ◽  
Individual Agent ◽  
Q Learning ◽  
Stochastic Environments ◽  
State Aggregation ◽  
Multi Agent ◽  
Fuzzy State ◽  
Better Than

Reinforcement learning is one of the more attractive machine learning technologies, due to its unsupervised learning structure and ability to continually learn even as the operating environment changes. Additionally, by applying reinforcement learning to multiple cooperative software agents (a multi-agent system) not only allows each individual agent to learn from its own experience, but also opens up the opportunity for the individual agents to learn from the other agents in the system, thus accelerating the rate of learning. This research presents the novel use of fuzzy state aggregation, as the means of function approximation, combined with the fastest policy hill climbing methods of Win or Lose Fast (WoLF) and policy-dynamics based WoLF (PD-WoLF). The combination of fast policy hill climbing and fuzzy state aggregation function approximation is tested in two stochastic environments: Tileworld and the simulated robot soccer domain, RoboCup. The Tileworld results demonstrate that a single agent using the combination of FSA and PHC learns quicker and performs better than combined fuzzy state aggregation and Q-learning reinforcement learning alone. Results from the multi-agent RoboCup domain again illustrate that the policy hill climbing algorithms perform better than Q-learning alone in a multi-agent environment. The learning is further enhanced by allowing the agents to share their experience through a weighted strategy sharing.

scholarly journals Efficient Actor-Critic Algorithm with Hierarchical Model Learning and Planning

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Shan Zhong ◽  
Quan Liu ◽  
QiMing Fu
Keyword(s):  
Convergence Rate ◽  
Hierarchical Model ◽  
Function Approximation ◽  
Local Linear Regression ◽  
Benchmark Problems ◽  
Time Step ◽  
Model Learning ◽  
Linear Function Approximation ◽  
Efficient Learning ◽  
The Value Function

To improve the convergence rate and the sample efficiency, two efficient learning methods AC-HMLP and RAC-HMLP (AC-HMLP withl2-regularization) are proposed by combining actor-critic algorithm with hierarchical model learning and planning. The hierarchical models consisting of the local and the global models, which are learned at the same time during learning of the value function and the policy, are approximated by local linear regression (LLR) and linear function approximation (LFA), respectively. Both the local model and the global model are applied to generate samples for planning; the former is used only if the state-prediction error does not surpass the threshold at each time step, while the latter is utilized at the end of each episode. The purpose of taking both models is to improve the sample efficiency and accelerate the convergence rate of the whole algorithm through fully utilizing the local and global information. Experimentally, AC-HMLP and RAC-HMLP are compared with three representative algorithms on two Reinforcement Learning (RL) benchmark problems. The results demonstrate that they perform best in terms of convergence rate and sample efficiency.

scholarly journals Soft Policy Gradient Method for Maximum Entropy Deep Reinforcement Learning

2019 ◽  
Author(s):  
Wenjie Shi ◽  
Shiji Song ◽  
Cheng Wu
Keyword(s):  
Reinforcement Learning ◽  
Maximum Entropy ◽  
Bellman Equation ◽  
Value Functions ◽  
Policy Actor ◽  
Model Free ◽  
Policy Gradient ◽  
Gradient Based ◽  
Continuous Actions ◽  
Stable Learning

Maximum entropy deep reinforcement learning (RL) methods have been demonstrated on a range of challenging continuous tasks. However, existing methods either suffer from severe instability when training on large off-policy data or cannot scale to tasks with very high state and action dimensionality such as 3D humanoid locomotion. Besides, the optimality of desired Boltzmann policy set for non-optimal soft value function is not persuasive enough. In this paper, we first derive soft policy gradient based on entropy regularized expected reward objective for RL with continuous actions. Then, we present an off-policy actor-critic, model-free maximum entropy deep RL algorithm called deep soft policy gradient (DSPG) by combining soft policy gradient with soft Bellman equation. To ensure stable learning while eliminating the need of two separate critics for soft value functions, we leverage double sampling approach to making the soft Bellman equation tractable. The experimental results demonstrate that our method outperforms in performance over off-policy prior methods.

Reinforcement learning vs. rule-based adaptive traffic signal control: A Fourier basis linear function approximation for traffic signal control

2021 ◽  
pp. 1-15
Author(s):  
Theresa Ziemke ◽  
Lucas N. Alegre ◽  
Ana L.C. Bazzan
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Function Approximation ◽  
Traffic Signals ◽  
The State ◽  
Signal Control ◽  
Traffic Signal Control ◽  
Rule Based ◽  
Fourier Basis ◽  
Linear Function Approximation

Reinforcement learning is an efficient, widely used machine learning technique that performs well when the state and action spaces have a reasonable size. This is rarely the case regarding control-related problems, as for instance controlling traffic signals. Here, the state space can be very large. In order to deal with the curse of dimensionality, a rough discretization of such space can be employed. However, this is effective just up to a certain point. A way to mitigate this is to use techniques that generalize the state space such as function approximation. In this paper, a linear function approximation is used. Specifically, SARSA ( λ ) with Fourier basis features is implemented to control traffic signals in the agent-based transport simulation MATSim. The results are compared not only to trivial controllers such as fixed-time, but also to state-of-the-art rule-based adaptive methods. It is concluded that SARSA ( λ ) with Fourier basis features is able to outperform such methods, especially in scenarios with varying traffic demands or unexpected events.

scholarly journals Scalable Initial State Interdiction for Factored MDPs

2018 ◽  
Author(s):  
Swetasudha Panda ◽  
Yevgeniy Vorobeychik
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Optimal Policy ◽  
Function Approximation ◽  
Stackelberg Game ◽  
Game Model ◽  
Initial State ◽  
Novel Approach ◽  
Linear Function Approximation ◽  
Computationally Expensive

We propose a novel Stackelberg game model of MDP interdiction in which the defender modifies the initial state of the planner, who then responds by computing an optimal policy starting with that state. We first develop a novel approach for MDP interdiction in factored state space that allows the defender to modify the initial state. The resulting approach can be computationally expensive for large factored MDPs. To address this, we develop several interdiction algorithms that leverage variations of reinforcement learning using both linear and non-linear function approximation. Finally, we extend the interdiction framework to consider a Bayesian interdiction problem in which the interdictor is uncertain about some of the planner's initial state features. Extensive experiments demonstrate the effectiveness of our approaches.

scholarly journals Minibatch Recursive Least Squares Q-Learning

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Chunyuan Zhang ◽  
Qi Song ◽  
Zeng Meng
Keyword(s):  
Reinforcement Learning ◽  
Least Squares ◽  
Linear Function ◽  
Function Approximation ◽  
Learning Algorithm ◽  
Learning Algorithms ◽  
Optimization Technique ◽  
Recursive Least Squares ◽  
Q Learning ◽  
Linear Function Approximation

The deep Q-network (DQN) is one of the most successful reinforcement learning algorithms, but it has some drawbacks such as slow convergence and instability. In contrast, the traditional reinforcement learning algorithms with linear function approximation usually have faster convergence and better stability, although they easily suffer from the curse of dimensionality. In recent years, many improvements to DQN have been made, but they seldom make use of the advantage of traditional algorithms to improve DQN. In this paper, we propose a novel Q-learning algorithm with linear function approximation, called the minibatch recursive least squares Q-learning (MRLS-Q). Different from the traditional Q-learning algorithm with linear function approximation, the learning mechanism and model structure of MRLS-Q are more similar to those of DQNs with only one input layer and one linear output layer. It uses the experience replay and the minibatch training mode and uses the agent’s states rather than the agent’s state-action pairs as the inputs. As a result, it can be used alone for low-dimensional problems and can be seamlessly integrated into DQN as the last layer for high-dimensional problems as well. In addition, MRLS-Q uses our proposed average RLS optimization technique, so that it can achieve better convergence performance whether it is used alone or integrated with DQN. At the end of this paper, we demonstrate the effectiveness of MRLS-Q on the CartPole problem and four Atari games and investigate the influences of its hyperparameters experimentally.

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