Receding Horizon Curiosity

Sample-efficient exploration is crucial not only for discovering rewarding experiences but also for adapting to environment changes in a task-agnostic fashion. A principled treatment of the problem of optimal input synthesis for system identification is provided within the framework of sequential Bayesian experimental design. In this paper, we present an effective trajectory-optimization-based approximate solution of this otherwise intractable problem that models optimal exploration in an unknown Markov decision process (MDP). By interleaving episodic exploration with Bayesian nonlinear system identification, our algorithm takes advantage of the inductive bias to explore in a directed manner, without assuming prior knowledge of the MDP. Empirical evaluations indicate a clear advantage of the proposed algorithm in terms of the rate of convergence and the final model fidelity when compared to intrinsic-motivation-based algorithms employing exploration bonuses such as prediction error and information gain. Moreover, our method maintains a computational advantage over a recent model-based active exploration (MAX) algorithm, by focusing on the information gain along trajectories instead of seeking a global exploration policy. A reference implementation of our algorithm and the conducted experiments is publicly available.

[1]  D. Lindley On a Measure of the Information Provided by an Experiment , 1956 .

[2]  A. A. Feldbaum,et al.  DUAL CONTROL THEORY, IV , 1961 .

[3]  Raman K. Mehra,et al.  Optimal input signals for parameter estimation in dynamic systems--Survey and new results , 1974 .

[4]  Martin B. Zarrop,et al.  Optimal experiment design for dynamic system identification , 1977 .

[5]  John N. Tsitsiklis,et al.  The Complexity of Markov Decision Processes , 1987, Math. Oper. Res..

[6]  Stewart W. Wilson,et al.  A Possibility for Implementing Curiosity and Boredom in Model-Building Neural Controllers , 1991 .

[7]  Jürgen Schmidhuber,et al.  Curious model-building control systems , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[8]  David A. Cohn,et al.  Active Learning with Statistical Models , 1996, NIPS.

[9]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[10]  Leslie Pack Kaelbling,et al.  Planning and Acting in Partially Observable Stochastic Domains , 1998, Artif. Intell..

[11]  E. Deci,et al.  Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions. , 2000, Contemporary educational psychology.

[12]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[13]  Michael Kearns,et al.  Near-Optimal Reinforcement Learning in Polynomial Time , 2002, Machine Learning.

[14]  Xavier Bombois,et al.  Input design: from open-loop to control-oriented design , 2006 .

[15]  Radford M. Neal Pattern Recognition and Machine Learning , 2007, Technometrics.

[16]  Benjamin Recht,et al.  Random Features for Large-Scale Kernel Machines , 2007, NIPS.

[17]  Andrew Y. Ng,et al.  Near-Bayesian exploration in polynomial time , 2009, ICML '09.

[18]  Burr Settles,et al.  Active Learning Literature Survey , 2009 .

[19]  Leslie Pack Kaelbling,et al.  Belief space planning assuming maximum likelihood observations , 2010, Robotics: Science and Systems.

[20]  Yi Sun,et al.  Planning to Be Surprised: Optimal Bayesian Exploration in Dynamic Environments , 2011, AGI.

[21]  Carl E. Rasmussen,et al.  PILCO: A Model-Based and Data-Efficient Approach to Policy Search , 2011, ICML.

[22]  P. Silvia Curiosity and Motivation , 2012 .

[23]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[24]  R. Ryan The Oxford Handbook of Human Motivation , 2012 .

[25]  Pieter Abbeel,et al.  Scaling up Gaussian Belief Space Planning Through Covariance-Free Trajectory Optimization and Automatic Differentiation , 2014, WAFR.

[26]  Shie Mannor,et al.  Bayesian Reinforcement Learning: A Survey , 2015, Found. Trends Mach. Learn..

[27]  Sergey Levine,et al.  Incentivizing Exploration In Reinforcement Learning With Deep Predictive Models , 2015, ArXiv.

[28]  Filip De Turck,et al.  VIME: Variational Information Maximizing Exploration , 2016, NIPS.

[29]  Tom Schaul,et al.  Unifying Count-Based Exploration and Intrinsic Motivation , 2016, NIPS.

[30]  Kian Hsiang Low,et al.  Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond , 2015, AAAI.

[31]  Philipp Hennig,et al.  Dual Control for Approximate Bayesian Reinforcement Learning , 2015, J. Mach. Learn. Res..

[32]  X. Huan,et al.  Sequential Bayesian optimal experimental design via approximate dynamic programming , 2016, 1604.08320.

[33]  Marc G. Bellemare,et al.  Count-Based Exploration with Neural Density Models , 2017, ICML.

[34]  Alexei A. Efros,et al.  Curiosity-Driven Exploration by Self-Supervised Prediction , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW).

[35]  Sham M. Kakade,et al.  Towards Generalization and Simplicity in Continuous Control , 2017, NIPS.

[36]  Sergey Levine,et al.  Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor , 2018, ICML.

[37]  Yuval Tassa,et al.  DeepMind Control Suite , 2018, ArXiv.

[38]  Amos J. Storkey,et al.  Exploration by Random Network Distillation , 2018, ICLR.

[39]  Wojciech Jaskowski,et al.  Model-Based Active Exploration , 2018, ICML.

[40]  Moritz Diehl,et al.  CasADi: a software framework for nonlinear optimization and optimal control , 2018, Mathematical Programming Computation.

[41]  Alexei A. Efros,et al.  Large-Scale Study of Curiosity-Driven Learning , 2018, ICLR.

[42]  P. Alam ‘A’ , 2021, Composites Engineering: An A–Z Guide.

[43]  T. L. Lai Andherbertrobbins Asymptotically Efficient Adaptive Allocation Rules , 2022 .