Quantizing a continuous POMDP into a finite MDP to preserve optimality

Naci Saldi; Serdar Yüksel; Tamás Linder, Asymptotic Optimality of Finite Model Approximations for Partially Observed Markov Decision Processes With Discounted Cost, IEEE Transactions on Automatic Control ( Volume: 65, Issue: 1, Jan. 2020), DOI: 10.1109/TAC.2019.2907172.

We consider finite model approximations of discrete-time partially observed Markov decision processes (POMDPs) under the discounted cost criterion. After converting the original partially observed stochastic control problem to a fully observed one on the belief space, the finite models are obtained through the uniform quantization of the state and action spaces of the belief space Markov decision process (MDP). Under mild assumptions on the components of the original model, it is established that the policies obtained from these finite models are nearly optimal for the belief space MDP, and so, for the original partially observed problem. The assumptions essentially require that the belief space MDP satisfies a mild weak continuity condition. We provide an example and introduce explicit approximation procedures for the quantization of the set of probability measures on the state space of POMDP (i.e., belief space).

A universal approximator for the value function in continuous-state VI

William B. Haskell; Rahul Jain; Hiteshi Sharma; Pengqian Yu, TA Universal Empirical Dynamic Programming Algorithm for Continuous State MDPs, IEEE Transactions on Automatic Control ( Volume: 65, Issue: 1, Jan. 2020), DOI: 10.1109/TAC.2019.2907414.

We propose universal randomized function approximation-based empirical value learning (EVL) algorithms for Markov decision processes. The “empirical” nature comes from each iteration being done empirically from samples available from simulations of the next state. This makes the Bellman operator a random operator. A parametric and a nonparametric method for function approximation using a parametric function space and a reproducing kernel Hilbert space respectively are then combined with EVL. Both function spaces have the universal function approximation property. Basis functions are picked randomly. Convergence analysis is performed using a random operator framework with techniques from the theory of stochastic dominance. Finite time sample complexity bounds are derived for both universal approximate dynamic programming algorithms. Numerical experiments support the versatility and computational tractability of this approach.

Do we prefer that our predictions fit observations -to validate our expectations- or that they surprise us -to acquire new knowledge-?

Clare Press, Peter Kok, Daniel Yon, The Perceptual Prediction Paradox, Trends in Cognitive Sciences, Volume 24, Issue 1, January 2020, Pages 4-6, DOI: 10.1016/j.tics.2019.11.003.

From the noisy information bombarding our senses, our brains must construct percepts that are veridical – reflecting the true state of the world – and informative – conveying what we did not already know. Influential theories suggest that both challenges are met through mechanisms that use expectations about the likely state of the world to shape perception. However, current models explaining how expectations render perception either veridical or informative are mutually incompatible. While the former propose that perceptual experiences are dominated by events we expect, the latter propose that perception of expected events is suppressed. To solve this paradox we propose a two-process model in which probabilistic knowledge initially biases perception towards what is likely and subsequently upweights events that are particularly surprising.

Similarities between motor control and cognitive control

Harrison Ritz, Romy Frömer, Amitai Shenhav, Bridging Motor and Cognitive Control: It’s About Time!, Trends in Cognitive Sciences, Volume 24, Issue 1, January 2020, Pages 4-6, DOI: 10.1016/j.tics.2019.11.005.

Is how we control our thoughts similar to how we control our movements? Egger et al. show that the neural dynamics underlying the control of internal states exhibit similar algorithmic properties as those that control movements. This experiment reveals a promising connection between how we control our brain and our body.

Interesting alternative to the classical “maximize expected utility” rule for decision making

EtienneKoechlin, Human Decision-Making beyond the Rational Decision Theory, Trends in Cognitive Sciences, Volume 24, Issue 1, January 2020, Pages 4-6, DOI: 10.1016/j.tics.2019.11.001.

Two recent studies (Farashahi et al. and Rouault et al.) provide compelling evidence refuting the Subjective Expected Utility (SEU) hypothesis as a ground model describing human decision-making. Together, these studies pave the way towards a new model that subsumes the notion of decision-making and adaptive behavior into a single account.

Nice related work on change-point detection and a novel algorithm for off-line detection of abrupt changes in multivariate signals

Charles Truong; Laurent Oudre; Nicolas Vayatis, Greedy Kernel Change-Point Detection, IEEE Transactions on Signal Processing ( Volume: 67, Issue: 24, Dec.15, 15 2019), DOI: 10.1109/TSP.2019.2953670.

We consider the problem of detecting abrupt changes in the underlying stochastic structure of multivariate signals. A novel non-parametric and model-free off-line change-point detection method based on a kernel mapping is presented. This approach is sequential and alternates between two steps: a greedy detection to estimate a new breakpoint and a projection to remove its contribution to the signal. The resulting algorithm is able to segment time series for which no accurate model is available: it is computationally more efficient than exact kernel change-point detection and more precise than window-based approximations. The proposed method also offers some theoretical consistency properties. For the special case of a linear kernel, an even faster implementation is provided. The proposed strategy is compared to standard parametric and non-parametric procedures on a real-world data set composed of 262 accelerometer recordings.

On the importance of dynamics and diversity in (cognitive) symbol systems

Tadahiro Taniguchi; Emre Ugur; Matej Hoffmann; Lorenzo Jamone; Takayuki Nagai; Benjamin Rosman, Symbol Emergence in Cognitive Developmental Systems: A Survey, IEEE Transactions on Cognitive and Developmental Systems ( Volume: 11, Issue: 4, Dec. 2019), DOI: 10.1109/TCDS.2018.2867772.

Humans use signs, e.g., sentences in a spoken language, for communication and thought. Hence, symbol systems like language are crucial for our communication with other agents and adaptation to our real-world environment. The symbol systems we use in our human society adaptively and dynamically change over time. In the context of artificial intelligence (AI) and cognitive systems, the symbol grounding problem has been regarded as one of the central problems related to symbols. However, the symbol grounding problem was originally posed to connect symbolic AI and sensorimotor information and did not consider many interdisciplinary phenomena in human communication and dynamic symbol systems in our society, which semiotics considered. In this paper, we focus on the symbol emergence problem, addressing not only cognitive dynamics but also the dynamics of symbol systems in society, rather than the symbol grounding problem. We first introduce the notion of a symbol in semiotics from the humanities, to leave the very narrow idea of symbols in symbolic AI. Furthermore, over the years, it became more and more clear that symbol emergence has to be regarded as a multifaceted problem. Therefore, second, we review the history of the symbol emergence problem in different fields, including both biological and artificial systems, showing their mutual relations. We summarize the discussion and provide an integrative viewpoint and comprehensive overview of symbol emergence in cognitive systems. Additionally, we describe the challenges facing the creation of cognitive systems that can be part of symbol emergence systems.

Interesting related work on internal models for action prediction and on the exploration/exploitation trade-off

Simón C. Smith; J. Michael Herrmann, Evaluation of Internal Models in Autonomous Learning, IEEE Transactions on Cognitive and Developmental Systems ( Volume: 11, Issue: 4, Dec. 2019), DOI: 10.1109/TCDS.2018.2865999.

Internal models (IMs) can represent relations between sensors and actuators in natural and artificial agents. In autonomous robots, the adaptation of IMs and the adaptation of the behavior are interdependent processes which have been studied under paradigms for self-organization of behavior such as homeokinesis. We compare the effect of various types of IMs on the generation of behavior in order to evaluate model quality across different behaviors. The considered IMs differ in the degree of flexibility and expressivity related to, respectively, learning speed and structural complexity of the model. We show that the different IMs generate different error characteristics which in turn lead to variations of the self-generated behavior of the robot. Due to the tradeoff between error minimization and complexity of the explored environment, we compare the models in the sense of Pareto optimality. Among the linear and nonlinear models that we analyze, echo-state networks achieve a particularly high performance which we explain as a result of the combination of fast learning and complex internal dynamics. More generally, we provide evidence that Pareto optimization is preferable in autonomous learning as it allows that a special solution can be negotiated in any particular environment.

Modelling robot motion sequences through context-free grammars

Rudolf Lioutikov, Guilherme Maeda, Filipe Veiga, Kristian Kersting, Jan Peters, Learning attribute grammars for movement primitive sequencing, The International Journal of Robotics Research, Vol 39, Issue 1, 2020, DOI: 10.1177/0278364919868279.

Movement primitives are a well studied and widely applied concept in modern robotics. However, composing primitives out of an existing library has shown to be a challenging problem. We propose the use of probabilistic context-free grammars to sequence a series of primitives to generate complex robot policies from a given library of primitives. The rule-based nature of formal grammars allows an intuitive encoding of hierarchically structured tasks. This hierarchical concept strongly connects with the way robot policies can be learned, organized, and re-used. However, the induction of context-free grammars has proven to be a complicated and yet unsolved challenge. We exploit the physical nature of robot movement primitives to restrict and efficiently search the grammar space. The grammar is learned by applying a Markov chain Monte Carlo optimization over the posteriors of the grammars given the observations. The proposal distribution is defined as a mixture over the probabilities of the operators connecting the search space. Moreover, we present an approach for the categorization of probabilistic movement primitives and discuss how the connectibility of two primitives can be determined. These characteristics in combination with restrictions to the operators guarantee continuous sequences while reducing the grammar space. In addition, a set of attributes and conditions is introduced that augments probabilistic context-free grammars in order to solve primitive sequencing tasks with the capability to adapt single primitives within the sequence. The method was validated on tasks that require the generation of complex sequences consisting of simple movement primitives using a seven-degree-of-freedom lightweight robotic arm.

Mixing human advice and reward functions for improving reinforcement learning of motor skills in robots with a nice related work on interactive RL

Carlos Celemin, Guilherme Maeda, Javier Ruiz-del-Solar, Jan Peters, Jens Kober, Reinforcement learning of motor skills using Policy Search and human corrective advice, The International Journal of Robotics Research, Vol 38, Issue 14, 2019, DOI: 10.1177/0278364919871998.

Robot learning problems are limited by physical constraints, which make learning successful policies for complex motor skills on real systems unfeasible. Some reinforcement learning methods, like Policy Search, offer stable convergence toward locally optimal solutions, whereas interactive machine learning or learning-from-demonstration methods allow fast transfer of human knowledge to the agents. However, most methods require expert demonstrations. In this work, we propose the use of human corrective advice in the actions domain for learning motor trajectories. Additionally, we combine this human feedback with reward functions in a Policy Search learning scheme. The use of both sources of information speeds up the learning process, since the intuitive knowledge of the human teacher can be easily transferred to the agent, while the Policy Search method with the cost/reward function take over for supervising the process and reducing the influence of occasional wrong human corrections. This interactive approach has been validated for learning movement primitives with simulated arms with several degrees of freedom in reaching via-point movements, and also using real robots in such tasks as “writing characters” and the ball-in-a-cup game. Compared with standard reinforcement learning without human advice, the results show that the proposed method not only converges to higher rewards when learning movement primitives, but also that the learning is sped up by a factor of 4–40 times, depending on the task.