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Title: Learning Human Postural Control with Hierarchical Acquisition Functions

Paper content:
Learning control policies in robotic tasks requires a large number of interactions due to small learning rates, bounds on the updates or unknown constraints.
In contrast humans can infer protective and safe solutions after a single failure or unexpected observation.
In order to reach similar performance, we developed a hierarchical Bayesian optimization algorithm that replicates the cognitive inference and memorization process for avoiding failures in motor control tasks.
A Gaussian Process implements the modeling and the sampling of the acquisition function.
This enables rapid learning with large learning rates while a mental replay phase ensures that policy regions that led to failures are inhibited during the sampling process.
The features of the hierarchical Bayesian optimization method are evaluated in a simulated and physiological humanoid postural balancing task.
We quantitatively compare the human learning performance to our learning approach by evaluating the deviations of the center of mass during training.
Our results show that we can reproduce the efficient learning of human subjects in postural control tasks which provides a testable model for future physiological motor control tasks.
In these postural control tasks, our method outperforms standard Bayesian Optimization in the number of interactions to solve the task, in the computational demands and in the frequency of observed failures.
Autonomous systems such as anthropomorphic robots or self-driving cars must not harm cooperating humans in co-worker scenarios, pedestrians on the road or them selves.
To ensure safe interactions with the environment state-of-the-art robot learning approaches are first applied to simulations and afterwards an expert selects final candidate policies to be run on the real system.
However, for most autonomous systems a fine-tuning phase on the real system is unavoidable to compensate for unmodelled dynamics, motor noise or uncertainties in the hardware fabrication.
Several strategies were proposed to ensure safe policy exploration.
In special tasks like in robot arm manipulation the operational space can be constrained, for example, in classical null-space control approaches Baerlocher & Boulic (1998) ; Slotine (1991) ; Choi & Kim (2000) ; Gienger et al. (2005) ; Saab et al. (2013) ; Modugno et al. (2016) or constraint black-box optimizer Hansen et al. (2003) ; Wierstra et al. (2008) ; Kramer et al. (2009) ; Sehnke et al. (2010) ; Arnold & Hansen (2012) .
While this null-space strategy works in controlled environments like research labs where the environmental conditions do not change, it fails in everyday life tasks as in humanoid balancing where the priorities or constraints that lead to hardware damages when falling are unknown.
Alternatively, limiting the policy updates by applying probabilistic bounds in the robot configuration or motor command space Bagnell & Schneider (2003) ; ; Rueckert et al. (2014) ; Abdolmaleki et al. (2015) ; Rueckert et al. (2013) were proposed.
These techniques do not assume knowledge about constraints.
Closely related are also Bayesian optimization techniques with modulated acquisition functions Gramacy & Lee (2010) ; Berkenkamp et al. (2016) ; Englert & Toussaint (2016) ; Shahriari et al. (2016) to avoid exploring policies that might lead to failures.
However, all these approaches do not avoid failures but rather an expert interrupts the learning process when it anticipates a potential dangerous situation.
Figure 1: Illustration of the hierarchical BO algorithm.
In standard BO (clock-wise arrow), a mapping from policy parameters to rewards is learned, i.e., φ → r ∈ R 1 .
We propose a hierarchical process, where first features κ are sampled and later used to predict the potential of policies conditioned on these features, φ|κ → r.
The red dots show the first five successive roll-outs in the feature and the policy space of a humanoid postural control task.
All the aforementioned strategies cannot avoid harming the system itself or the environment without thorough experts knowledge, controlled environmental conditions or human interventions.
As humans require just few trials to perform reasonably well, it is desired to enable robots to reach similar performance even for high-dimensional problems.
Thereby, most approaches are based on the assumption of a "low effective dimensionality", thus most dimensions of a high-dimensional problem do not change the objective function significantly.
In Chen et al. (2012) a method for relevant variable selection based on Hierarchical Diagonal Sampling for both, variable selection and function optimization, has been proposed.
Randomization combined with Bayesian Optimization is proposed in Wang et al. (2013) to exploit effectively the aforementioned "low effective dimensionality".
In Li et al. (2018) a dropout algorithm has been introduced to overcome the high-dimensionality problem by only train onto a subset of variables in each iteration, evaluating a "regret gap" and providing strategies to reduce this gap efficiently.
In Rana et al. (2017) an algorithm has been proposed which optimizes an acquisition function by building new Gaussian Processes with sufficiently large kernellengths scales.
This ensures significant gradient updates in the acquisition function to be able to use gradient-dependent methods for optimization.
The contribution of this paper is a computational model for psychological motor control experiments based on hierarchical acquisition functions in Bayesian Optimization (HiBO).
Our motor skill learning method uses features for optimization to significantly reduce the number of required roll-outs.
In the feature space, we search for the optimum of the acquisition function by sampling and later use the best feature configuration to optimize the policy parameters which are conditioned on the given features, see also Figure 1 .
In postural control experiments, we show that our approach reduces the number of required roll-outs significantly compared to standard Bayesian Optimization.
The focus of this study is to develop a testable model for psychological motor control experiments where well known postural control features could be used.
These features are listed in Table 3 .
In future work we will extend our model to autonomous feature learning and will validate the approach in more challenging robotic tasks where 'good' features are hard to hand-craft.
We introduced HiBO, a hierarchical approach for Bayesian Optimization.
We showed that HiBO outperforms standard BO in a complex humanoid postural control task.
Moreover, we demonstrated the effects of the choice of the features and for different number of mental replay episodes.
We compared our results to the learning performance of real humans at the same task.
We found that the learning behavior is similar.
We found that our proposed hierarchical BO algorithm can reproduce the rapid motor adaptation of human subjects.
In contrast standard BO, our comparison method, is about four times slower.
In future work, we will examine the problem of simultaneously learning task relevant features in neural nets.

assistant: text: This paper presents a computational model for efficient human postural control adaptation based on hierarchical acquisition functions with well-known features.