복잡하고 불확실한 환경에서 최적 의사 결정을 위한 효율적인 로봇 학습

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·정보공학부, 2021. 2. Songhwai Oh.The problem of sequential decision making under an uncertain and complex environment is a long-standing challenging problem in robotics. In this thesis, we focus on learning a policy function of robotic systems for sequential decision making under which is called a robot learning framework. In particular, we are interested in reducing the sample complexity of the robot learning framework. Hence, we develop three sample efficient robot learning frameworks. The first one is the maximum entropy reinforcement learning. The second one is a perturbation-based exploration. The last one is learning from demonstrations with mixed qualities. For maximum entropy reinforcement learning, we employ a generalized Tsallis entropy regularization as an efficient exploration method. Tsallis entropy generalizes Shannon-Gibbs entropy by introducing a entropic index. By changing an entropic index, we can control the sparsity and multi-modality of policy. Based on this fact, we first propose a sparse Markov decision process (sparse MDP) which induces a sparse and multi-modal optimal policy distribution. In this MDP, the sparse entropy, which is a special case of Tsallis entropy, is employed as a policy regularization. We first analyze the optimality condition of a sparse MDP. Then, we propose dynamic programming methods for the sparse MDP and prove their convergence and optimality. We also show that the performance error of a sparse MDP has a constant bound, while the error of a soft MDP increases logarithmically with respect to the number of actions, where this performance error is caused by the introduced regularization term. Furthermore, we generalize sparse MDPs to a new class of entropy-regularized Markov decision processes (MDPs), which will be referred to as Tsallis MDPs, and analyzes different types of optimal policies with interesting properties related to the stochasticity of the optimal policy by controlling the entropic index. Furthermore, we also develop perturbation based exploration methods to handle heavy-tailed noises. In many robot learning problems, a learning signal is often corrupted by noises such as sub-Gaussian noise or heavy-tailed noise. While most of the exploration strategies have been analyzed under sub-Gaussian noise assumption, there exist few methods for handling such heavy-tailed rewards. Hence, to overcome heavy-tailed noise, we consider stochastic multi-armed bandits with heavy-tailed rewards. First, we propose a novel robust estimator that does not require prior information about a noise distribution, while other existing robust estimators demand prior knowledge. Then, we show that an error probability of the proposed estimator decays exponentially fast. Using this estimator, we propose a perturbation-based exploration strategy and develop a generalized regret analysis scheme that provides upper and lower regret bounds by revealing the relationship between the regret and the cumulative density function of the perturbation. From the proposed analysis scheme, we obtain gap-dependent and gap-independent upper and lower regret bounds of various perturbations. We also find the optimal hyperparameters for each perturbation, which can achieve the minimax optimal regret bound with respect to total rounds. For learning from demonstrations with mixed qualities, we develop a novel inverse reinforcement learning framework using leveraged Gaussian processes (LGP) which can handle negative demonstrations. In LGP, the correlation between two Gaussian processes is captured by a leveraged kernel function. By using properties, the proposed inverse reinforcement learning algorithm can learn from both positive and negative demonstrations. While most existing inverse reinforcement learning (IRL) methods suffer from the lack of information near low reward regions, the proposed method alleviates this issue by incorporating negative demonstrations. To mathematically formulate negative demonstrations, we introduce a novel generative model which can generate both positive and negative demonstrations using a parameter, called proficiency. Moreover, since we represent a reward function using a leveraged Gaussian process which can model a nonlinear function, the proposed method can effectively estimate the structure of a nonlinear reward function.본 학위 논문에서는 시범과 보상함수를 기반으로한 로봇 학습 문제를 다룬다. 로봇 학습 방법은 불확실하고 복잡 업무를 잘 수행 할 수 있는 최적의 정책 함수를 찾는 것을 목표로 한다. 로봇 학습 분야의 다양한 문제 중에, 샘플 복잡도를 줄이는 것에 집중한다. 특히, 효율적인 탐색 방법과 혼합 시범으로 부터의 학습 기법을 개발하여 적은 수의 샘플로도 높은 효율을 갖는 정책 함수를 학습하는 것이 목표이다. 효율적인 탐색 방법을 개발하기 위해서, 우리는 일반화된 쌀리스 엔트로피를 사용한다. 쌀리스 엔트로피는 샤논-깁스 엔트로피를 일반화한 개념으로 엔트로픽 인덱스라는 새로운 파라미터를 도입한다. 엔트로픽 인덱스를 조절함에 따라 다양한 형태의 엔트로피를 만들어 낼 수 있고 각 엔트로피는 서로 다른 레귤러라이제이션 효과를 보인다. 이 성질을 기반으로, 스파스 마르코프 결정과정을 제안한다. 스파스 마르코프 결정과정은 스파스 쌀리스 엔트로피를 이용하여 희소하면서 동시에 다모드의 정책 분포를 표현하는데 효과적이다. 이를 통해서 샤논-깁스 엔트로피를 사용하였을때에 비해 더 좋은 성능을 갖음을 수학적으로 증명하였다. 또한 스파스 쌀리스 엔트로피로 인한 성능 저하를 이론적으로 계산하였다. 스파스 마르코프 결정과정을 더욱 일반화시켜 일반화된 쌀리스 엔트로피 결정과정을 제안하였다. 마찬가지로 쌀리스 엔트로피를 마르코프 결정과정에 추가함으로써 생기는 최적 정책함수의 변화와 성능 저하를 수학적으로 증명하였다. 나아가, 성능저하를 없앨 수 있는 방법인 엔트로픽 인덱스 스케쥴링을 제안하였고 실험적으로 최적의 성능을 갖음을 보였다. 또한, 헤비테일드 잡음이 있는 학습 문제를 해결하기 위해서 외란(Perturbation)을 이용한 탐색 기법을 개발하였다. 로봇 학습의 많은 문제는 잡음의 영향이 존재한다. 학습 신호안에 다양한 형태로 잡음이 들어있는 경우가 있고 이러한 경우에 잡음을 제거 하면서 최적의 행동을 찾는 문제는 효율적인 탐사 기법을 필요로 한다. 기존의 방법론들은 서브 가우시안(sub-Gaussian) 잡음에만 적용 가능했다면, 본 학위 논문에서 제안한 방식은 헤비테일드 잡음을 해결 할 수 있다는 점에서 기존의 방법론들보다 장점을 갖는다. 먼저, 일반적인 외란에 대해서 리그렛 바운드를 증명하였고 외란의 누적분포함수(CDF)와 리그렛 사이의 관계를 증명하였다. 이 관계를 이용하여 다양한 외란 분포의 리그렛 바운드를 계산 가능하게 하였고 다양한 분포들의 가장 효율적인 탐색 파라미터를 계산하였다. 혼합시범으로 부터의 학습 기법을 개발하기 위해서, 오시범을 다룰 수 있는 새로운 형태의 가우시안 프로세스 회귀분석 방식을 개발하였고, 이 방식을 확장하여 레버리지 가우시안 프로세스 역강화학습 기법을 개발하였다. 개발된 기법에서는 정시범으로부터 무엇을 해야 하는지와 오시범으로부터 무엇을 하면 안되는지를 모두 학습할 수 있다. 기존의 방법에서는 쓰일 수 없었던 오시범을 사용 할 수 있게 만듦으로써 샘플 복잡도를 줄일 수 있었고 정제된 데이터를 수집하지 않아도 된다는 점에서 큰 장점을 갖음을 실험적으로 보였다.1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . 4 2 Background 5 2.1 Learning from Rewards . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Multi-Armed Bandits . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Contextual Multi-Armed Bandits . . . . . . . . . . . . . . . 7 2.1.3 Markov Decision Processes . . . . . . . . . . . . . . . . . . 9 2.1.4 Soft Markov Decision Processes . . . . . . . . . . . . . . . . 10 2.2 Learning from Demonstrations . . . . . . . . . . . . . . . . . . . . 12 2.2.1 Behavior Cloning . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Inverse Reinforcement Learning . . . . . . . . . . . . . . . . 13 3 Sparse Policy Learning 19 3.1 Sparse Policy Learning for Reinforcement Learning . . . . . . . . . 19 3.1.1 Sparse Markov Decision Processes . . . . . . . . . . . . . . 23 3.1.2 Sparse Value Iteration . . . . . . . . . . . . . . . . . . . . . 29 3.1.3 Performance Error Bounds for Sparse Value Iteration . . . 30 3.1.4 Sparse Exploration and Update Rule for Sparse Deep QLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Sparse Policy Learning for Imitation Learning . . . . . . . . . . . . 46 3.2.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2.2 Principle of Maximum Causal Tsallis Entropy . . . . . . . . 50 3.2.3 Maximum Causal Tsallis Entropy Imitation Learning . . . 54 3.2.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4 Entropy-based Exploration 65 4.1 Generalized Tsallis Entropy Reinforcement Learning . . . . . . . . 65 4.1.1 Maximum Generalized Tsallis Entropy in MDPs . . . . . . 71 4.1.2 Dynamic Programming for Tsallis MDPs . . . . . . . . . . 74 4.1.3 Tsallis Actor Critic for Model-Free RL . . . . . . . . . . . . 78 4.1.4 Experiments Setup . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . 84 4.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.2 E cient Exploration for Robotic Grasping . . . . . . . . . . . . . . 92 4.2.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.2.2 Shannon Entropy Regularized Neural Contextual Bandit Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.2.3 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . 99 4.2.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . 104 4.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5 Perturbation-Based Exploration 113 5.1 Perturbed Exploration for sub-Gaussian Rewards . . . . . . . . . . 115 5.1.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.1.2 Heavy-Tailed Perturbations . . . . . . . . . . . . . . . . . . 117 5.1.3 Adaptively Perturbed Exploration . . . . . . . . . . . . . . 119 5.1.4 General Regret Bound for Sub-Gaussian Rewards . . . . . . 120 5.1.5 Regret Bounds for Speci c Perturbations with sub-Gaussian Rewards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2 Perturbed Exploration for Heavy-Tailed Rewards . . . . . . . . . . 128 5.2.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.2.2 Sub-Optimality of Robust Upper Con dence Bounds . . . . 132 5.2.3 Adaptively Perturbed Exploration with A p-Robust Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2.4 General Regret Bound for Heavy-Tailed Rewards . . . . . . 136 5.2.5 Regret Bounds for Speci c Perturbations with Heavy-Tailed Rewards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.2.6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 144 5.2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6 Inverse Reinforcement Learning with Negative Demonstrations149 6.1 Leveraged Gaussian Processes Inverse Reinforcement Learning . . 151 6.1.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . 152 6.1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.1.3 Gaussian Process Regression . . . . . . . . . . . . . . . . . 156 6.1.4 Leveraged Gaussian Processes . . . . . . . . . . . . . . . . . 159 6.1.5 Gaussian Process Inverse Reinforcement Learning . . . . . 164 6.1.6 Inverse Reinforcement Learning with Leveraged Gaussian Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.1.7 Simulations and Experiment . . . . . . . . . . . . . . . . . 175 6.1.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 7 Conclusion 185 Appendices 189 A Proofs of Chapter 3.1. 191 A.1 Useful Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 A.2 Sparse Bellman Optimality Equation . . . . . . . . . . . . . . . . . 192 A.3 Sparse Tsallis Entropy . . . . . . . . . . . . . . . . . . . . . . . . . 195 A.4 Upper and Lower Bounds for Sparsemax Operation . . . . . . . . . 196 A.5 Comparison to Log-Sum-Exp . . . . . . . . . . . . . . . . . . . . . 200 A.6 Convergence and Optimality of Sparse Value Iteration . . . . . . . 201 A.7 Performance Error Bounds for Sparse Value Iteration . . . . . . . . 203 B Proofs of Chapter 3.2. 209 B.1 Change of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 209 B.2 Concavity of Maximum Causal Tsallis Entropy . . . . . . . . . . . 210 B.3 Optimality Condition of Maximum Causal Tsallis Entropy . . . . . 212 B.4 Interpretation as Robust Bayes . . . . . . . . . . . . . . . . . . . . 215 B.5 Generative Adversarial Setting with Maximum Causal Tsallis Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 B.6 Tsallis Entropy of a Mixture of Gaussians . . . . . . . . . . . . . . 217 B.7 Causal Entropy Approximation . . . . . . . . . . . . . . . . . . . . 218 C Proofs of Chapter 4.1. 221 C.1 q-Maximum: Bounded Approximation of Maximum . . . . . . . . . 223 C.2 Tsallis Bellman Optimality Equation . . . . . . . . . . . . . . . . . 226 C.3 Variable Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 C.4 Tsallis Bellman Optimality Equation . . . . . . . . . . . . . . . . . 230 C.5 Tsallis Policy Iteration . . . . . . . . . . . . . . . . . . . . . . . . . 234 C.6 Tsallis Bellman Expectation (TBE) Equation . . . . . . . . . . . . 234 C.7 Tsallis Bellman Expectation Operator and Tsallis Policy Evaluation235 C.8 Tsallis Policy Improvement . . . . . . . . . . . . . . . . . . . . . . 237 C.9 Tsallis Value Iteration . . . . . . . . . . . . . . . . . . . . . . . . . 239 C.10 Performance Error Bounds . . . . . . . . . . . . . . . . . . . . . . 241 C.11 q-Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 D Proofs of Chapter 4.2. 245 D.1 In nite Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 D.2 Regret Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 E Proofs of Chapter 5.1. 255 E.1 General Regret Lower Bound of APE . . . . . . . . . . . . . . . . . 255 E.2 General Regret Upper Bound of APE . . . . . . . . . . . . . . . . 257 E.3 Proofs of Corollaries . . . . . . . . . . . . . . . . . . . . . . . . . . 266 F Proofs of Chapter 5.2. 279 F.1 Regret Lower Bound for Robust Upper Con dence Bound . . . . . 279 F.2 Bounds on Tail Probability of A p-Robust Estimator . . . . . . . . 284 F.3 General Regret Upper Bound of APE2 . . . . . . . . . . . . . . . . 287 F.4 General Regret Lower Bound of APE2 . . . . . . . . . . . . . . . . 299 F.5 Proofs of Corollaries . . . . . . . . . . . . . . . . . . . . . . . . . . 302Docto

Quantum Hamiltonian Learning Using Imperfect Quantum Resources

Identifying an accurate model for the dynamics of a quantum system is a vexing problem that underlies a range of problems in experimental physics and quantum information theory. Recently, a method called quantum Hamiltonian learning has been proposed by the present authors that uses quantum simulation as a resource for modeling an unknown quantum system. This approach can, under certain circumstances, allow such models to be efficiently identified. A major caveat of that work is the assumption of that all elements of the protocol are noise-free. Here, we show that quantum Hamiltonian learning can tolerate substantial amounts of depolarizing noise and show numerical evidence that it can tolerate noise drawn from other realistic models. We further provide evidence that the learning algorithm will find a model that is maximally close to the true model in cases where the hypothetical model lacks terms present in the true model. Finally, we also provide numerical evidence that the algorithm works for non-commuting models. This work illustrates that quantum Hamiltonian learning can be performed using realistic resources and suggests that even imperfect quantum resources may be valuable for characterizing quantum systems.Comment: 16 pages 11 Figure

Reinforcement learning for robotic manipulation using simulated locomotion demonstrations

Mastering robotic manipulation skills through reinforcement learning (RL) typically requires the design of shaped reward functions. Recent developments in this area have demonstrated that using sparse rewards, i.e. rewarding the agent only when the task has been successfully completed, can lead to better policies. However, state-action space exploration is more difficult in this case. Recent RL approaches to learning with sparse rewards have leveraged high-quality human demonstrations for the task, but these can be costly, time consuming or even impossible to obtain. In this paper, we propose a novel and effective approach that does not require human demonstrations. We observe that every robotic manipulation task could be seen as involving a locomotion task from the perspective of the object being manipulated, i.e. the object could learn how to reach a target state on its own. In order to exploit this idea, we introduce a framework whereby an object locomotion policy is initially obtained using a realistic physics simulator. This policy is then used to generate auxiliary rewards, called simulated locomotion demonstration rewards (SLDRs), which enable us to learn the robot manipulation policy. The proposed approach has been evaluated on 13 tasks of increasing complexity, and can achieve higher success rate and faster learning rates compared to alternative algorithms. SLDRs are especially beneficial for tasks like multi-object stacking and non-rigid object manipulation

Cieran: Designing Sequential Colormaps via In-Situ Active Preference Learning

Quality colormaps can help communicate important data patterns. However, finding an aesthetically pleasing colormap that looks "just right" for a given scenario requires significant design and technical expertise. We introduce Cieran, a tool that allows any data analyst to rapidly find quality colormaps while designing charts within Jupyter Notebooks. Our system employs an active preference learning paradigm to rank expert-designed colormaps and create new ones from pairwise comparisons, allowing analysts who are novices in color design to tailor colormaps to their data context. We accomplish this by treating colormap design as a path planning problem through the CIELAB colorspace with a context-specific reward model. In an evaluation with twelve scientists, we found that Cieran effectively modeled user preferences to rank colormaps and leveraged this model to create new quality designs. Our work shows the potential of active preference learning for supporting efficient visualization design optimization.Comment: CHI 2024. 12 pages/9 figure

A Survey on Causal Reinforcement Learning

While Reinforcement Learning (RL) achieves tremendous success in sequential decision-making problems of many domains, it still faces key challenges of data inefficiency and the lack of interpretability. Interestingly, many researchers have leveraged insights from the causality literature recently, bringing forth flourishing works to unify the merits of causality and address well the challenges from RL. As such, it is of great necessity and significance to collate these Causal Reinforcement Learning (CRL) works, offer a review of CRL methods, and investigate the potential functionality from causality toward RL. In particular, we divide existing CRL approaches into two categories according to whether their causality-based information is given in advance or not. We further analyze each category in terms of the formalization of different models, ranging from the Markov Decision Process (MDP), Partially Observed Markov Decision Process (POMDP), Multi-Arm Bandits (MAB), and Dynamic Treatment Regime (DTR). Moreover, we summarize the evaluation matrices and open sources while we discuss emerging applications, along with promising prospects for the future development of CRL.Comment: 29 pages, 20 figure

Using Multi-Relational Embeddings as Knowledge Graph Representations for Robotics Applications

User demonstrations of robot tasks in everyday environments, such as households, can be brittle due in part to the dynamic, diverse, and complex properties of those environments. Humans can find solutions in ambiguous or unfamiliar situations by using a wealth of common-sense knowledge about their domains to make informed generalizations. For example, likely locations for food in a novel household. Prior work has shown that robots can benefit from reasoning about this type of semantic knowledge, which can be modeled as a knowledge graph of interrelated facts that define whether a relationship exists between two entities. Semantic reasoning about domain knowledge using knowledge graph representations has improved the robustness and usability of end user robots by enabling more fault tolerant task execution. Knowledge graph representations define the underlying representation of facts, how facts are organized, and implement semantic reasoning by defining the possible computations over facts (e.g. association, fact-prediction). This thesis examines the use of multi-relational embeddings as knowledge graph representations within the context of robust task execution and develops methods to explain the inferences of and sequentially train multi-relational embeddings. This thesis contributes: (i) a survey of knowledge graph representations that model semantic domain knowledge in robotics, (ii) the development and evaluation of our knowledge graph representation based on multi-relational embeddings, (iii) the integration of our knowledge graph representation into a robot architecture to improve robust task execution, (iv) the development and evaluation of methods to sequentially update multi-relational embeddings, and (v) the development and evaluation of an inference reconciliation framework for multi-relational embeddings.Ph.D