Temporal Difference Algorithm Research Articles

A model for automatic agent generation based on machine learning in simulation games

With the continuous promotion of Artificial Intelligence (AI) technology in games, researchers are generally willing to pay attention to the effect of AI on game picture quality and man-machine games. However, how to generate a large number of non-player characters (NPC) in a game, especially in a simulation game, is still a problem. Even if some people use machine learning to discover solutions, most answers tend to be limited to copying finite-state machines established by programmers. This paper explores techniques, such as machine learning and maze algorithms, for 2D in-game environments to construct a model that can quickly generate NPCs with 'personality' and adapt to the environment when developing a game. In the process of model construction, the temporal difference algorithm and the depth-first algorithm are used to customize the decision structure for the NPC. At the same time, a simple node-style map generation algorithm is added to restrain NPC. Moreover, an optional neural network model gives the NPC a memory that can be updated. This model successfully realizes the rapid construction of NPC in developing some simple 2D games. In addition, NPCs have a fair amount of intelligence. It can be used during game development or while the game is running and generate a certain number of NPCs in an unfamiliar environment with differences in behavior.

Online attentive kernel-based temporal difference learning

Kernel-based reinforcement learning has received increasing attention because it requires less prior knowledge linear approximation and neural networks. Online kernel-based updating, however, is hindered by the challenge of catastrophic forgetting or interference. Sparse representation is a key method to address this issue, but existing methods fail to satisfy four criteria: learnability, nonprior, nontruncation, and explicitness. In this paper, we present an attentive kernel-based value function approximation as a learnable, nonprior, nontruncated, and explicit sparse representation. We propose the online attentive kernel-based temporal difference (OAKTD) algorithm, which employs two-timescale optimization, and provide a convergence analysis for our proposed algorithm. Experimental results show that OAKTD outperforms online kernel-based TD learning algorithms, and the TD learning algorithm with Tile Coding on classical tasks, i.e., Mountain Car, Acrobot, CartPole and Puddle World.

Provable distributed adaptive temporal-difference learning over time-varying networks

Multi-agent reinforcement learning (MARL) has been successfully applied in many fields. In MARL, the policy evaluation problem is one of crucial problems. In order to solve this problem, distributed Temporal-Difference (TD) learning algorithm is one of the most popular methods in a cooperative manner. Despite its empirical success, however, the theory of the adaptive variant of distributed TD learning still remain limited. To fill this gap, we propose an adaptive distributed temporal-difference algorithm (referred to as MS-ADTD) under Markovian sampling over time-varying networks. Furthermore, we rigorously analyze the convergence of MS-ADTD, the theoretical results show that the local estimation can converge linearly to the optimal neighborhood. Meanwhile, the theoretical results are verified by simulation experiments.

Accelerated and Instance-Optimal Policy Evaluation with Linear Function Approximation

We study the problem of policy evaluation with linear function approximation and present efficient and practical algorithms that come with strong optimality guarantees. We begin by proving lower bounds that establish baselines on both the deterministic error and stochastic error in this problem. In particular, we prove an oracle complexity lower bound on the deterministic error in an instance-dependent norm associated with the stationary distribution of the transition kernel, and we use the local asymptotic minimax machinery to prove an instance-dependent lower bound on the stochastic error in the independent and identically distributed (i.i.d.) observation model. Existing algorithms fail to match at least one of these lower bounds: To illustrate, we analyze a variance-reduced variant of temporal difference learning, showing in particular that it fails to achieve the oracle complexity lower bound. To remedy this issue, we develop an accelerated, variance-reduced fast temporal difference (VRFTD) algorithm that simultaneously matches both lower bounds and attains a strong notion of instance-optimality. Finally, we extend the VRFTD algorithm to the setting with Markovian observations and provide instance-dependent convergence results. Our theoretical guarantees of optimality are corroborated by numerical experiments.

Uncertainty maximization in partially observable domains: A cognitive perspective

Faced with an ever-increasing complexity of their domains of application, artificial learning agents are now able to scale up in their ability to process an overwhelming amount of data. However, this comes at the cost of encoding and processing an increasing amount of redundant information. This work exploits the possibility of learning systems, applied in partially observable domains, to selectively focus on the specific type of information that is more likely related to the causal interaction among transitioning states. A temporal difference displacement criterion is defined to implement adaptive masking of the observations. It can enable a significant improvement of convergence of temporal difference algorithms applied to partially observable Markov processes, as shown by experiments performed under a variety of machine learning problems, ranging from highly complex visuals as Atari games to simple textbook control problems such as CartPole. The proposed framework can be added to most RL algorithms since it only affects the observation process, selecting the parts more promising to explain the dynamics of the environment and reducing the dimension of the observation space.

Learning Rat-Like Behavioral Interaction Using a Small-Scale Robotic Rat.

In this paper, we propose a novel method for emulating rat-like behavioral interactions in robots using reinforcement learning. Specifically, we develop a state decision method to optimize the interaction process among 6 known behavior types that have been identified in previous research on rat interactions. The novelty of our method lies in using the temporal difference (TD) algorithm to optimize the state decision process, which enables the robots to make informed decisions about their behavior choices. To assess the similarity between robot and rat behavior, we use Pearson correlation. We then use TD-λ to update the state value function and make state decisions based on probability. The robots execute these decisions using our dynamics-based controller. Our results demonstrate that our method can generate rat-like behaviors on both short- and long-term timescales, with interaction information entropy comparable to that between real rats. Overall, our approach shows promise for controlling robots in robot-rat interactions and highlights the potential of using reinforcement learning to develop more sophisticated robotic systems.

Double Deep Q-Network with Dynamic Bootstrapping for Real-Time Isolated Signal Control: A Traffic Engineering Perspective

Real-time isolated signal control (RISC) at an intersection is of interest in the field of traffic engineering. Energizing RISC with reinforcement learning (RL) is feasible and necessary. Previous studies paid less attention to traffic engineering considerations and under-utilized traffic expertise to construct RL tasks. This study profiles the single-ring RISC problem from the perspective of traffic engineers, and improves a prevailing RL method for solving it. By qualitative applicability analysis, we choose double deep Q-network (DDQN) as the basic method. A single agent is deployed for an intersection. Reward is defined with vehicle departures to properly encourage and punish the agent’s behavior. The action is to determine the remaining green time for the current vehicle phase. State is represented in a grid-based mode. To update action values in time-varying environments, we present a temporal-difference algorithm TD(Dyn) to perform dynamic bootstrapping with the variable interval between actions selected. To accelerate training, we propose a data augmentation based on intersection symmetry. Our improved DDQN, termed D3ynQN, is subject to the signal timing constraints in engineering. The experiments at a close-to-reality intersection indicate that, by means of D3ynQN and non-delay-based reward, the agent acquires useful knowledge to significantly outperform a fully-actuated control technique in reducing average vehicle delay.

Gradient Temporal Difference with Momentum: Stability and Convergence

Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy ball momentum term and provide choice of step size and momentum parameter that ensures almost sure convergence of these algorithms asymptotically. In doing so, we decompose the heavy ball Gradient TD iterates into three separate iterates with different step sizes. We first analyze these iterates under one-timescale SA setting using results from current literature. However, the one-timescale case is restrictive and a more general analysis can be provided by looking at a three-timescale decomposition of the iterates. In the process we provide the first conditions for stability and convergence of general three-timescale SA. We then prove that the heavy ball Gradient TD algorithm is convergent using our three-timescale SA analysis. Finally, we evaluate these algorithms on standard RL problems and report improvement in performance over the vanilla algorithms.

Simple and Optimal Methods for Stochastic Variational Inequalities, II: Markovian Noise and Policy Evaluation in Reinforcement Learning

The focus of this paper is on stochastic variational inequalities (VI) under Markovian noise. A prominent application of our algorithmic developments is the stochastic policy evaluation problem in reinforcement learning. Prior investigations in the literature focused on temporal difference (TD) learning by employing nonsmooth finite time analysis motivated by stochastic subgradient descent leading to certain limitations. These encompass the requirement of analyzing a modified TD algorithm that involves projection to an a-priori defined Euclidean ball, achieving a non-optimal convergence rate and no clear way of deriving the beneficial effects of parallel implementation. Our approach remedies these shortcomings in the broader context of stochastic VIs and in particular when it comes to stochastic policy evaluation. We developed a variety of simple TD learning type algorithms motivated by its original version that maintain its simplicity, while offering distinct advantages from a non-asymptotic analysis point of view. We first provide an improved analysis of the standard TD algorithm that can benefit from parallel implementation. Then we present versions of a conditional TD algorithm (CTD), that involves periodic updates of the stochastic iterates, which reduce the bias and therefore exhibit improved iteration complexity. This brings us to the fast TD (FTD) algorithm which combines elements of CTD and the stochastic operator extrapolation method of the companion paper. For a novel index resetting policy FTD exhibits the best known convergence rate. We also devised a robust version of the algorithm that is particularly suitable for discounting factors close to 1.

Choice-selective sequences dominate in cortical relative to thalamic inputs to NAc to support reinforcement learning.

SUMMARYHow are actions linked with subsequent outcomes to guide choices? The nucleus accumbens, which is implicated in this process, receives glutamatergic inputs from the prelimbic cortex and midline regions of the thalamus. However, little is known about whether and how representations differ across these input pathways. By comparing these inputs during a reinforcement learning task in mice, we discovered that prelimbic cortical inputs preferentially represent actions and choices, whereas midline thalamic inputs preferentially represent cues. Choice-selective activity in the prelimbic cortical inputs is organized in sequences that persist beyond the outcome. Through computational modeling, we demonstrate that these sequences can support the neural implementation of reinforcement-learning algorithms, in both a circuit model based on synaptic plasticity and one based on neural dynamics. Finally, we test and confirm a prediction of our circuit models by direct manipulation of nucleus accumbens input neurons.

Joint control of manufacturing and onsite microgrid system via novel neural-network integrated reinforcement learning algorithms

Microgrid is a promising technology of distributed energy supply system, which consists of storage devices, generation capacities including renewable sources, and controllable loads. It has been widely investigated and applied for residential and commercial end-use customers as well as critical facilities. In this paper, we propose a joint state-based dynamic control model on microgrids and manufacturing systems where optimal controls for both sides are implemented to coordinate the energy demand and supply so that the overall production cost can be minimized considering the constraint of production target. Markov Decision Process (MDP) is used to formulate the decision-making procedure. The main computing challenge to solve the formulated MDP lies in the co-existence of both discrete and continuous parts of the high-dimensional state/action space that are intertwined with constraints. A novel reinforcement learning algorithm that leverages both Temporal Difference (TD) and Deterministic Policy Gradient (DPG) algorithms is proposed to address the computation challenge. Experiments for a manufacturing system with an onsite microgrid system with renewable sources have been implemented to justify the effectiveness of the proposed method.

Reinforcement learning: Dopamine ramps with fuzzy value estimates

A new study in reinforcement learning theory shows that extending the temporal difference algorithm to unbiased learning under state uncertainty explains the observed ramping behaviour of dopamine neurons.

Toward the biological model of the hippocampus as the successor representation agent

The hippocampus is an essential brain region for spatial memory and learning. Recently, a theoretical model of the hippocampus based on temporal difference (TD) learning has been published. Inspired by the successor representation (SR) learning algorithms, which decompose value function of TD learning into reward and state transition, they argued that the rate of firing of CA1 place cells in the hippocampus represents the probability of state transition. This theory, called predictive map theory, claims that the hippocampus representing space learns the probability of transition from the current state to the future state. The neural correlates of expecting the future state are the firing rates of the CA1 place cells. This explanation is plausible for the results recorded in behavioral experiments, but it is lacking the neurobiological implications.Modifying the SR learning algorithm added biological implications to the predictive map theory. Similar with the simultaneous needs of information of the current and future state in the SR learning algorithm, the CA1 place cells receive two inputs from CA3 and entorhinal cortex. Mathematical transformation showed that the SR learning algorithm is equivalent to the heterosynaptic plasticity rule. The heterosynaptic plasticity phenomena in CA1 were discussed and compared with the modified SR update rule. This study attempted to interpret the TD algorithm as the neurobiological mechanism occurring in place learning, and to integrate the neuroscience and artificial intelligence approaches in the field.

Reinforcement learning in optimization problems. Applications to geophysical data inversion

<abstract> <p>In this paper, we introduce a novel inversion methodology that combines the benefits offered by Reinforcement-Learning techniques with the advantages of the Epsilon-Greedy method for an expanded exploration of the model space. Among the various Reinforcement Learning approaches, we applied the set of algorithms included in the category of the Q-Learning methods. We show that the Temporal Difference algorithm offers an effective iterative approach that allows finding an optimal solution in geophysical inverse problems. Furthermore, the Epsilon-Greedy method properly coupled with the Reinforcement Learning workflow, allows expanding the exploration of the model-space, minimizing the misfit between observed and predicted responses and limiting the problem of local minima of the cost function. In order to prove the feasibility of our methodology, we tested it using synthetic geo-electric data and a seismic refraction data set available in the public domain.</p> </abstract>

Distributed Value Function Approximation for Collaborative Multiagent Reinforcement Learning

In this article, we propose several novel distributed gradient-based temporal-difference algorithms for multiagent off-policy learning of linear approximation of the value function in Markov decision processes with strict information structure constraints, limiting interagent communications to small neighborhoods. The algorithms are composed of the following: first, local parameter updates based on the single-agent off-policy gradient temporal-difference learning algorithms, including the eligibility traces with state-dependent parameters and, second, linear stochastic time-varying consensus schemes, represented by directed graphs. The proposed algorithms differ in their form, definition of eligibility traces, selection of time scales, and the way of incorporating consensus iterations. The main contribution of this article is a convergence analysis based on the general properties of the underlying Feller-Markov processes and the stochastic time-varying consensus model. We prove under general assumptions that the parameter estimates generated by all the proposed algorithms weakly converge to the corresponding ordinary differential equations with precisely defined invariant sets. It is demonstrated how the adopted methodology can be applied to temporal-difference algorithms under weaker information structure constraints. The variance reduction effect of the proposed algorithms is demonstrated by formulating and analyzing an asymptotic stochastic differential equation. Specific guidelines for the communication network design are provided. The algorithms' superior properties are illustrated by characteristic simulation results.

Dynamical systems as a level of cognitive analysis of multi-agent learning

A dynamical systems perspective on multi-agent learning, based on the link between evolutionary game theory and reinforcement learning, provides an improved, qualitative understanding of the emerging collective learning dynamics. However, confusion exists with respect to how this dynamical systems account of multi-agent learning should be interpreted. In this article, I propose to embed the dynamical systems description of multi-agent learning into different abstraction levels of cognitive analysis. The purpose of this work is to make the connections between these levels explicit in order to gain improved insight into multi-agent learning. I demonstrate the usefulness of this framework with the general and widespread class of temporal-difference reinforcement learning. I find that its deterministic dynamical systems description follows a minimum free-energy principle and unifies a boundedly rational account of game theory with decision-making under uncertainty. I then propose an on-line sample-batch temporal-difference algorithm which is characterized by the combination of applying a memory-batch and separated state-action value estimation. I find that this algorithm serves as a micro-foundation of the deterministic learning equations by showing that its learning trajectories approach the ones of the deterministic learning equations under large batch sizes. Ultimately, this framework of embedding a dynamical systems description into different abstraction levels gives guidance on how to unleash the full potential of the dynamical systems approach to multi-agent learning.

Optimal control for semi‐Markov jump linear systems via TP‐free temporal difference () learning

AbstractIn the present study, a temporal difference (TD) learning algorithm is proposed to solve the optimal control problem for semi‐Markov jump linear systems (S‐MJLSs). The proposed scheme is TP‐free so that it can be applied in cases without pre‐known transition probabilities of embedded Markov chain. Coupled algebraic Riccati equations (CAREs) implied with the analytical solution of control gains are derived by utilizing a S‐MJLS augmented with maximum sojourn time, which contributes to develop the TD learning algorithm. It is proved that for sufficiently rich enough jumping modes and jumping numbers observed online, the value function in TD algorithm converges to CAREs solutions. Finally, an example is carried out to evaluate the learning capability of TD algorithm and the effectiveness of the proposed control method.

Foresee then Evaluate: Decomposing Value Estimation with Latent Future Prediction

Value function is the central notion of Reinforcement Learning (RL). Value estimation, especially with function approximation, can be challenging since it involves the stochasticity of environmental dynamics and reward signals that can be sparse and delayed in some cases. A typical model-free RL algorithm usually estimates the values of a policy by Temporal Difference (TD) or Monte Carlo (MC) algorithms directly from rewards, without explicitly taking dynamics into consideration. In this paper, we propose Value Decomposition with Future Prediction (VDFP), providing an explicit two-step understanding of the value estimation process: 1) first foresee the latent future, 2) and then evaluate it. We analytically decompose the value function into a latent future dynamics part and a policy-independent trajectory return part, inducing a way to model latent dynamics and returns separately in value estimation. Further, we derive a practical deep RL algorithm, consisting of a convolutional model to learn compact trajectory representation from past experiences, a conditional variational auto-encoder to predict the latent future dynamics and a convex return model that evaluates trajectory representation. In experiments, we empirically demonstrate the effectiveness of our approach for both off-policy and on-policy RL in several OpenAI Gym continuous control tasks as well as a few challenging variants with delayed reward.

Concentration bounds for temporal difference learning with linear function approximation: the case of batch data and uniform sampling

We propose a stochastic approximation (SA) based method with randomization of samples for policy evaluation using the least squares temporal difference (LSTD) algorithm. Our proposed scheme is equivalent to running regular temporal difference learning with linear function approximation, albeit with samples picked uniformly from a given dataset. Our method results in an O(d) improvement in complexity in comparison to LSTD, where d is the dimension of the data. We provide non-asymptotic bounds for our proposed method, both in high probability and in expectation, under the assumption that the matrix underlying the LSTD solution is positive definite. The latter assumption can be easily satisfied for the pathwise LSTD variant proposed by Lazaric (J Mach Learn Res 13:3041–3074, 2012). Moreover, we also establish that using our method in place of LSTD does not impact the rate of convergence of the approximate value function to the true value function. These rate results coupled with the low computational complexity of our method make it attractive for implementation in big data settings, where d is large. A similar low-complexity alternative for least squares regression is well-known as the stochastic gradient descent (SGD) algorithm. We provide finite-time bounds for SGD. We demonstrate the practicality of our method as an efficient alternative for pathwise LSTD empirically by combining it with the least squares policy iteration algorithm in a traffic signal control application. We also conduct another set of experiments that combines the SA-based low-complexity variant for least squares regression with the LinUCB algorithm for contextual bandits, using the large scale news recommendation dataset from Yahoo.

Byzantine-Resilient Decentralized Policy Evaluation With Linear Function Approximation

This paper considers the policy evaluation problem in a multi-agent reinforcement learning (MARL) environment over decentralized and directed networks. The focus is on decentralized temporal difference (TD) learning with linear function approximation in the presence of unreliable or even malicious agents, termed as Byzantine agents. In order to evaluate the quality of a fixed policy in a common environment, agents usually run decentralized TD($\lambda$) collaboratively. However, when some Byzantine agents behave adversarially, decentralized TD($\lambda$) is unable to learn an accurate linear approximation for the true value function. We propose a trimmed-mean based Byzantine-resilient decentralized TD($\lambda$) algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error in the presence of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm.