Potential-based Reward Shaping Research Articles

Potential-based reward shaping using state–space segmentation for efficiency in reinforcement learning

Reinforcement Learning (RL) algorithms encounter slow learning in environments with sparse explicit reward structures due to the limited feedback available on the agent’s behavior. This problem is exacerbated particularly in complex tasks with large state and action spaces. To address this inefficiency, in this paper, we propose a novel approach based on potential-based reward-shaping using state–space segmentation to decompose the task and to provide more frequent feedback to the agent. Our approach involves extracting state–space segments by formulating the problem as a minimum cut problem on a transition graph, constructed using the agent’s experiences during interactions with the environment via the Extended Segmented Q-Cut algorithm. Subsequently, these segments are leveraged in the agent’s learning process through potential-based reward shaping. Our experimentation on benchmark problem domains with sparse rewards demonstrated that our proposed method effectively accelerates the agent’s learning without compromising computation time while upholding the policy invariance principle.

Potential-Based Reward Shaping for Intrinsic Motivation (Student Abstract)

Recently there has been a proliferation of intrinsic motivation (IM) reward shaping methods to learn in complex and sparse-reward environments. These methods can often inadvertently change the set of optimal policies in an environment, leading to suboptimal behavior. Previous work on mitigating the risks of reward shaping, particularly through potential-based reward shaping (PBRS), has not been applicable to many IM methods, as they are often complex, trainable functions themselves, and therefore dependent on a wider set of variables than the traditional reward functions that PBRS was developed for. We present an extension to PBRS that we show preserves the set of optimal policies under a more general set of functions than has been previously demonstrated. We also present Potential-Based Intrinsic Motivation (PBIM), a method for converting IM rewards into a potential-based form that are useable without altering the set of optimal policies. Testing in the MiniGrid DoorKey environment, we demonstrate that PBIM successfully prevents the agent from converging to a suboptimal policy and can speed up training.

Reinforcement Learning Control With Knowledge Shaping.

We aim at creating a transfer reinforcement learning framework that allows the design of learning controllers to leverage prior knowledge extracted from previously learned tasks and previous data to improve the learning performance of new tasks. Toward this goal, we formalize knowledge transfer by expressing knowledge in the value function in our problem construct, which is referred to as reinforcement learning with knowledge shaping (RL-KS). Unlike most transfer learning studies that are empirical in nature, our results include not only simulation verifications but also an analysis of algorithm convergence and solution optimality. Also different from the well-established potential-based reward shaping methods which are built on proofs of policy invariance, our RL-KS approach allows us to advance toward a new theoretical result on positive knowledge transfer. Furthermore, our contributions include two principled ways that cover a range of realization schemes to represent prior knowledge in RL-KS. We provide extensive and systematic evaluations of the proposed RL-KS method. The evaluation environments not only include classical RL benchmark problems but also include a challenging task of real-time control of a robotic lower limb with a human user in the loop.

Cooperative multi-agent game based on reinforcement learning

Multi-agent reinforcement learning holds tremendous potential for revolutionizing intelligent systems across diverse domains. However, it is also concomitant with a set of formidable challenges, which include the effective allocation of credit values to each agent, real-time collaboration among heterogeneous agents, and an appropriate reward function to guide agent behavior. To handle these issues, we propose an innovative solution named the Graph Attention Counterfactual Multiagent Actor–Critic algorithm (GACMAC). This algorithm encompasses several key components: First, it employs a multi-agent actor–critic framework along with counterfactual baselines to assess the individual actions of each agent. Second, it integrates a graph attention network to enhance real-time collaboration among agents, enabling heterogeneous agents to effectively share information during handling tasks. Third, it incorporates prior human knowledge through a potential-based reward shaping method, thereby elevating the convergence speed and stability of the algorithm. We tested our algorithm on the StarCraft Multi-Agent Challenge (SMAC) platform, which is a recognized platform for testing multi-agent algorithms, and our algorithm achieved a win rate of over 95% on the platform, comparable to the current state-of-the-art multi-agent controllers.

Reward shaping using directed graph convolution neural networks for reinforcement learning and games

Game theory can employ reinforcement learning algorithms to identify the optimal policy or equilibrium solution. Potential-based reward shaping (PBRS) methods are prevalently used for accelerating reinforcement learning, ensuring the optimal policy remains consistent. Existing PBRS research performs message passing based on graph convolution neural networks (GCNs) to propagate information from rewarding states. However, in an irreversible time-series reinforcement learning problem, undirected graphs will not only mislead message-passing schemes but also lose a distinctive direction structure. In this paper, a novel approach called directed graph convolution neural networks for reward shaping φDCN has been proposed to tackle this problem. The key innovation of φDCN is the extension of spectral-based undirected graph convolution to directed graphs. Messages can be efficiently propagated by leveraging a directed graph Laplacian as a substitute for the state transition matrix. As a consequence, potential-based reward shaping can then be implemented by the propagated messages. The incorporation of temporal dependencies between states makes φDCN more suitable for real-world scenarios than existing potential-based reward shaping methods based on undirected graph convolutional networks. Preliminary experiments demonstrate that the proposed φDCN exhibits a substantial improvement compared to other competing algorithms on both Atari and MuJoCo benchmarks.

GRL-PS: Graph Embedding-Based DRL Approach for Adaptive Path Selection

Forwarding path selection for data traffic is one of the most fundamental operations in computer networks, whose performance drastically impacts both transmission efficiency and reliability in network domains. Although deep reinforcement learning (DRL) has attracted considerable attention for path selection instead of hand-tuned heuristics, few works have considered how to exploit graph-structured information in networks to improve routing and forwarding efficiency. In fact, generating routes is essentially a process for finding a subgraph in a graph-structured network. To this end, this paper proposes an effective and novel graph embedding-based DRL framework for adaptive path selection (termed GRL-PS), aiming at reducing end-to-end (E2E) latency and promoting network throughput while maintaining stability in dynamically changing environments. Specifically, graph representation learning (GRL) is deployed as an effective enabler for the DRL agent to learn the relational knowledge of interacting entities for route decisions in networks. However, training such an agent in a dynamically changing environment encounters a knowledge acquisition bottleneck, since the DRL agent is always forced to learn every task from scratch. To improve the adaptation of behaviors and acquire skills beyond what the source policy can teach, we introduce potential-based reward shaping as a means of knowledge transfer to guide the agent in unfamiliar conditions with sparse rewards. Experimental results show that compared with baseline methods, our solution can achieve nearly-optimal performance with both latency and throughput, especially in large-scale dynamic networks.

Reward shaping using convolutional neural network

In this paper, we propose Value Iteration Network for Reward Shaping (VIN-RS), a potential-based reward shaping mechanism using Convolutional Neural Network (CNN). The proposed VIN-RS embeds a CNN trained on computed labels using the message passing mechanism of the Hidden Markov Model. The CNN processes images or graphs of the environment to predict the shaping values. Recent work on reward shaping still has limitations towards training on a representation of the Markov Decision Process (MDP) and building an estimate of the transition matrix. The advantage of VIN-RS is to construct an effective potential function from an estimated MDP while automatically inferring the environment transition matrix. The proposed VIN-RS estimates the transition matrix through a self-learned convolution filter while extracting environment details from the input frames or sampled graphs. Due to (1) the previous success of using message passing for reward shaping; and (2) the CNN planning behavior, we use these messages to train the CNN of VIN-RS. Experiments are performed on tabular games, Atari 2600 and MuJoCo, for discrete and continuous action space. Our results illustrate promising improvements in the learning speed and maximum cumulative reward compared to the state-of-the-art. The improvement achieved by VIN-RS can only be observed for some of the games due to the underlying nature of some environments. In terms of the studied MuJoCo games, there is on average an increase of 30% in the maximum reward reached during early stages of learning.

Graph learning-based generation of abstractions for reinforcement learning

AbstractThe application of reinforcement learning (RL) algorithms is often hindered by the combinatorial explosion of the state space. Previous works have leveraged abstractions which condense large state spaces to find tractable solutions. However, they assumed that the abstractions are provided by a domain expert. In this work, we propose a new approach to automatically construct abstract Markov decision processes (AMDPs) for potential-based reward shaping to improve the sample efficiency of RL algorithms. Our approach to constructing abstract states is inspired by graph representation learning methods, it effectively encodes the topological and reward structure of the ground-level MDP. We perform large-scale quantitative experiments on a range of navigation and gathering tasks under both stationary and stochastic settings. Our approach shows improvements of up to 8.5 times in sample efficiency and up to 3 times in run time over the baseline approach. Besides, with our qualitative analyses of the generated AMDPs, we are able to visually demonstrate the capability of our approach to preserve the topological and reward structure of the ground-level MDP.

Learning Potential in Subgoal-Based Reward Shaping

Human knowledge can reduce the number of iterations required to learn in reinforcement learning. Though the most common approach uses trajectories, it is difficult to acquire them in certain domains. Subgoals, which are intermediate states, have been studied instead of trajectories. Subgoal-based reward shaping is a reward-shaping framework with a sequence of subgoals based on potential-based reward shaping. The potential function which is a component of potential-based reward shaping has a hyperparameter that controls its output. However, it is not easy to select a hyperparameter because its appropriate value depends on the reward function of an environment, and the reward function is unknown. We propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">learned potential</i> that parameterizes a hyperparameter and acquires its potential through learning. A value is an expected accumulated reward if an agent follows its policy after the current state and is strongly related to the reward function. With learned potential, we build an abstract state space with a sequence of subgoals and use the value over the abstract states as the potential to accelerate the value learning. N-step TD learning learns the values over the abstract state. We conducted experiments to evaluate the effectiveness of learned potential, and the results indicate its effectiveness compared with a baseline reinforcement learning algorithm and several reward-shaping algorithms. The results also indicate that the participants’ subgoals are superior to subgoals generated randomly with learned potential. We discuss the appropriate number of subgoals for learned potential, that partially ordered subgoal is helpful for learned potential, that learned potential cannot make learning efficient in step penalized rewards, and that learned potential is superior to the non-learned potential in mixed positive and negative rewards.

Graph convolutional recurrent networks for reward shaping in reinforcement learning

In this paper, we consider the problem of low-speed convergence in Reinforcement Learning (RL). As a solution, various potential-based reward shaping techniques were proposed to form the potential function. Learning a potential function is still challenging and comparable to building a value function from scratch. In this work, our main contribution is proposing a new scheme for reward shaping, which combines (1) the Graph Convolutional Recurrent Networks (GCRN), (2) augmented Krylov, and (3) look-ahead advice to form the potential function. We propose an architecture for GCRN that combines Graph Convolutional Networks (GCN) to capture spatial dependencies and Bi-Directional Gated Recurrent Units (Bi-GRUs) to account for temporal dependencies. Our definition of the loss function of GCRN incorporates the message passing technique of the Hidden Markov Models (HMM). Since the transition matrix of the environment is hard to compute, we use the Krylov basis to estimate the transition matrix, which outperforms the existing approximation bases. Unlike existing potential functions that only rely on states to perform reward shaping, we use both the states and actions through the look-ahead advice mechanism to produce more precise advice. Our evaluations conducted on the Atari 2600 and MuJoCo games show that our solution outperforms the state-of-the-art that utilizes GCN as the potential function in most games in terms of the learning speed while reaching higher rewards.

A Safe and Efficient Lane Change Decision-Making Strategy of Autonomous Driving Based on Deep Reinforcement Learning

As an indispensable branch of machine learning (ML), reinforcement learning (RL) plays a prominent role in the decision-making process of autonomous driving (AD), which enables autonomous vehicles (AVs) to learn an optimal driving strategy through continuous interaction with the environment. This paper proposes a deep reinforcement learning (DRL)-based motion planning strategy for AD tasks in the highway scenarios where an AV merges into two-lane road traffic flow and realizes the lane changing (LC) maneuvers. We integrate the DRL model into the AD system relying on the end-to-end learning method. An improved DRL algorithm based on deep deterministic policy gradient (DDPG) is developed with well-defined reward functions. In particular, safety rules (SR), safety prediction (SP) module and trauma memory (TM) as well as the dynamic potential-based reward shaping (DPBRS) function are adopted to further enhance safety and accelerate learning of the LC behavior. For validation, the proposed DSSTD algorithm is trained and tested on the dual-computer co-simulation platform. The comparative experimental results show that our proposal outperforms other benchmark algorithms in both driving safety and efficiency.

Reward shaping to improve the performance of deep reinforcement learning in perishable inventory management

Deep reinforcement learning (DRL) has proven to be an effective, general-purpose technology to develop ‘good’ replenishment policies in inventory management. We show how transfer learning from existing, well-performing heuristics may stabilize the training process and improve the performance of DRL in inventory control. While the idea is general, we specifically implement potential-based reward shaping to a deep Q-network algorithm to manage inventory of perishable goods that, cursed by dimensionality, has proven to be notoriously complex. The application of our approach may not only improve inventory cost performance and reduce computational effort, the increased training stability may also help to gain trust in the policies obtained by black box DRL algorithms.

Policy invariant explicit shaping: an efficient alternative to reward shaping

Reinforcement learning (RL) is a powerful learning paradigm in which agents can learn to maximize sparse and delayed reward signals. Although RL has had many impressive successes in complex domains, learning can take hours, days, or even years of training data. A major challenge of contemporary RL research is to discover how to learn with less data. Previous work has shown that domain information can be successfully used to shape the reward; by adding additional reward information, the agent can learn with much less data. Furthermore, if the reward is constructed from a potential function, the optimal policy is guaranteed to be unaltered. While such potential-based reward shaping (PBRS) holds promise, it is limited by the need for a well-defined potential function. Ideally, we would like to be able to take arbitrary advice from a human or other agent and improve performance without affecting the optimal policy. The recently introduced dynamic potential-based advice (DPBA) was proposed to tackle this challenge by predicting the potential function values as part of the learning process. However, this article demonstrates theoretically and empirically that, while DPBA can facilitate learning with good advice, it does in fact alter the optimal policy. We further show that when adding the correction term to “fix” DPBA it no longer shows effective shaping with good advice. We then present a simple method called policy invariant explicit shaping (PIES) and show theoretically and empirically that PIES can use arbitrary advice, speed-up learning, and leave the optimal policy unchanged.

Subgoal-Based Reward Shaping to Improve Efficiency in Reinforcement Learning

Reinforcement learning, which acquires a policy maximizing long-term rewards, has been actively studied. Unfortunately, this learning type is too slow and difficult to use in practical situations because the state-action space becomes huge in real environments. Many studies have incorporated human knowledge into reinforcement Learning. Though human knowledge on trajectories is often used, a human could be asked to control an AI agent, which can be difficult. Knowledge on subgoals may lessen this requirement because humans need only to consider a few representative states on an optimal trajectory in their minds. The essential factor for learning efficiency is rewards. Potential-based reward shaping is a basic method for enriching rewards. However, it is often difficult to incorporate subgoals for accelerating learning over potential-based reward shaping. This is because the appropriate potentials are not intuitive for humans. We extend potential-based reward shaping and propose a subgoal-based reward shaping. The method makes it easier for human trainers to share their knowledge of subgoals. To evaluate our method, we obtained a subgoal series from participants and conducted experiments in three domains, four-rooms(discrete states and discrete actions), pinball(continuous and discrete), and picking(both continuous). We compared our method with a baseline reinforcement learning algorithm and other subgoal-based methods, including random subgoal and naive subgoal-based reward shaping. As a result, we found out that our reward shaping outperformed all other methods in learning efficiency.

Reward Shaping to Improve the Performance of Deep Reinforcement Learning in Inventory Management

Deep reinforcement learning (DRL) has proven to be an effective, general-purpose technology to develop 'good' replenishment policies in inventory management. We show how transfer learning from existing, well-performing heuristics may stabilize the training process and improve the performance of DRL in inventory control. While the idea is general, we specifically implement potential-based reward shaping to a deep Q-network algorithm to manage inventory of perishable goods that, cursed by dimensionality, has proven to be notoriously complex. The application of our approach may not only improve inventory cost performance and reduce computational effort, the increased training stability may also help to gain trust in the policies obtained by black box DRL algorithms.

Maneuver Strategy Generation of UCAV for within Visual Range Air Combat Based on Multi-Agent Reinforcement Learning and Target Position Prediction

With the development of unmanned combat air vehicles (UCAVs) and artificial intelligence (AI), within visual range (WVR) air combat confrontations utilizing intelligent UCAVs are expected to be widely used in future air combats. As controlling highly dynamic and uncertain WVR air combats from the ground stations of the UCAV is not feasible, it is necessary to develop an algorithm that can generate highly intelligent air combat strategies in order to enable UCAV to independently complete air combat missions. In this paper, a 1-vs.-1 WVR air combat strategy generation algorithm is proposed using the multi-agent deep deterministic policy gradient (MADDPG). A 1-vs.-1 WVR air combat is modeled as a two-player zero-sum Markov game (ZSMG). A method for predicting the position of the target is introduced into the model in order to enable the UCAV to predict the target’s actions and position. Moreover, to ensure that the UCAV is not limited by the constraints of the basic fighter maneuver (BFM) library, the action space is considered to be a continuous one. At the same time, a potential-based reward shaping method is proposed in order to improve the efficiency of the air combat strategy generation algorithm. Finally, the efficiency of the air combat strategy generation algorithm and the intelligence level of the resulting strategy is verified through simulation experiments. The results show that an air combat strategy using target position prediction is superior to the one that does not use target position prediction.

Accelerating Interactive Reinforcement Learning by Human Advice for an Assembly Task by a Cobot

The assembly industry is shifting more towards customizable products, or requiring assembly of small batches. This requires a lot of reprogramming, which is expensive because a specialized engineer is required. It would be an improvement if untrained workers could help a cobot to learn an assembly sequence by giving advice. Learning an assembly sequence is a hard task for a cobot, because the solution space increases drastically when the complexity of the task increases. This work introduces a novel method where human knowledge is used to reduce this solution space, and as a result increases the learning speed. The method proposed is the IRL-PBRS method, which uses Interactive Reinforcement Learning (IRL) to learn from human advice in an interactive way, and uses Potential Based Reward Shaping (PBRS), in a simulated environment, to focus learning on a smaller part of the solution space. The method was compared in simulation to two other feedback strategies. The results show that IRL-PBRS converges more quickly to a valid assembly sequence policy and does this with the fewest human interactions. Finally, a use case is presented where participants were asked to program an assembly task. Here, the results show that IRL-PBRS learns quickly enough to keep up with advice given by a user, and is able to adapt online to a changing knowledge base.

IntrospectiveQ-learning and learning from demonstration

AbstractOne challenge faced by reinforcement learning (RL) agents is that in many environments the reward signal is sparse, leading to slow improvement of the agent’s performance in early learning episodes. Potential-based reward shaping can help to resolve the aforementioned issue of sparse reward by incorporating an expert’s domain knowledge into the learning through a potential function. Past work on reinforcement learning from demonstration (RLfD) directly mapped (sub-optimal) human expert demonstration to a potential function, which can speed up RL. In this paper we propose an introspective RL agent that significantly further speeds up the learning. An introspective RL agent records its state–action decisions and experience during learning in a priority queue. Good quality decisions, according to a Monte Carlo estimation, will be kept in the queue, while poorer decisions will be rejected. The queue is then used as demonstration to speed up RL via reward shaping. A human expert’s demonstration can be used to initialize the priority queue before the learning process starts. Experimental validation in the 4-dimensional CartPole domain and the 27-dimensional Super Mario AI domain shows that our approach significantly outperforms non-introspective RL and state-of-the-art approaches in RLfD in both domains.

Reward shaping for knowledge-based multi-objective multi-agent reinforcement learning

AbstractThe majority of multi-agent reinforcement learning (MARL) implementations aim to optimize systems with respect to a single objective, despite the fact that many real-world problems are inherently multi-objective in nature. Research into multi-objective MARL is still in its infancy, and few studies to date have dealt with the issue of credit assignment. Reward shaping has been proposed as a means to address the credit assignment problem in single-objective MARL, however it has been shown to alter the intended goals of a domain if misused, leading to unintended behaviour. Two popular shaping methods are potential-based reward shaping and difference rewards, and both have been repeatedly shown to improve learning speed and the quality of joint policies learned by agents in single-objective MARL domains. This work discusses the theoretical implications of applying these shaping approaches to cooperative multi-objective MARL problems, and evaluates their efficacy using two benchmark domains. Our results constitute the first empirical evidence that agents using these shaping methodologies can sample true Pareto optimal solutions in cooperative multi-objective stochastic games.

Policy invariance under reward transformations for multi-objective reinforcement learning

Reinforcement Learning (RL) is a powerful and well-studied Machine Learning paradigm, where an agent learns to improve its performance in an environment by maximising a reward signal. In multi-objective Reinforcement Learning (MORL) the reward signal is a vector, where each component represents the performance on a different objective. Reward shaping is a well-established family of techniques that have been successfully used to improve the performance and learning speed of RL agents in single-objective problems. The basic premise of reward shaping is to add an additional shaping reward to the reward naturally received from the environment, to incorporate domain knowledge and guide an agent’s exploration. Potential-Based Reward Shaping (PBRS) is a specific form of reward shaping that offers additional guarantees. In this paper, we extend the theoretical guarantees of PBRS to MORL problems. Specifically, we provide theoretical proof that PBRS does not alter the true Pareto front in both single- and multi-agent MORL. We also contribute the first published empirical studies of the effect of PBRS in single- and multi-agent MORL problems.