Wendelin Böhmer

Moritz A. Zanger, Wendelin Böhmer, Matthijs T. J. Spaan

In contrast to classical reinforcement learning (RL), distributional RL algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, we study the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and VizDoom and find that diverse projection ensembles lead to significant performance improvements over existing methods on a variety of tasks with the most pronounced gains in directed exploration problems.

Yaniv Oren, Villiam Vadocz, Matthijs T. J. Spaan et al.

The AlphaZero/MuZero (A/MZ) family of algorithms has achieved remarkable success across various challenging domains by integrating Monte Carlo Tree Search (MCTS) with learned models. Learned models introduce epistemic uncertainty, which is caused by learning from limited data and is useful for exploration in sparse reward environments. MCTS does not account for the propagation of this uncertainty however. To address this, we introduce Epistemic MCTS (EMCTS): a theoretically motivated approach to account for the epistemic uncertainty in search and harness the search for deep exploration. In the challenging sparse-reward task of writing code in the Assembly language {\sc subleq}, AZ paired with our method achieves significantly higher sample efficiency over baseline AZ. Search with EMCTS solves variations of the commonly used hard-exploration benchmark Deep Sea - which baseline A/MZ are practically unable to solve - much faster than an otherwise equivalent method that does not use search for uncertainty estimation, demonstrating significant benefits from search for epistemic uncertainty estimation.

Max Weltevrede, Matthijs T. J. Spaan, Wendelin Böhmer

In reinforcement learning (RL), key components of many algorithms are the exploration strategy and replay buffer. These strategies regulate what environment data is collected and trained on and have been extensively studied in the RL literature. In this paper, we investigate the impact of these components in the context of generalisation in multi-task RL. We investigate the hypothesis that collecting and training on more diverse data from the training environments will improve zero-shot generalisation to new tasks. We motivate mathematically and show empirically that generalisation to tasks that are "reachable'' during training is improved by increasing the diversity of transitions in the replay buffer. Furthermore, we show empirically that this same strategy also shows improvement for generalisation to similar but "unreachable'' tasks which could be due to improved generalisation of the learned latent representations.

Grigorii Veviurko, Wendelin Böhmer, Mathijs de Weerdt

Predict and optimize is an increasingly popular decision-making paradigm that employs machine learning to predict unknown parameters of optimization problems. Instead of minimizing the prediction error of the parameters, it trains predictive models using task performance as a loss function. The key challenge to train such models is the computation of the Jacobian of the solution of the optimization problem with respect to its parameters. For linear problems, this Jacobian is known to be zero or undefined; hence, approximations are usually employed. For non-linear convex problems, however, it is common to use the exact Jacobian. This paper demonstrates that the zero-gradient problem appears in the non-linear case as well -- the Jacobian can have a sizeable null space, thereby causing the training process to get stuck in suboptimal points. Through formal proofs, this paper shows that smoothing the feasible set resolves this problem. Combining this insight with known techniques from the literature, such as quadratic programming approximation and projection distance regularization, a novel method to approximate the Jacobian is derived. In simulation experiments, the proposed method increases the performance in the non-linear case and at least matches the existing state-of-the-art methods for linear problems.

Álvaro Serra-Gómez, Eduardo Montijano, Wendelin Böhmer et al.

In this paper, we consider the problem where a drone has to collect semantic information to classify multiple moving targets. In particular, we address the challenge of computing control inputs that move the drone to informative viewpoints, position and orientation, when the information is extracted using a "black-box" classifier, e.g., a deep learning neural network. These algorithms typically lack of analytical relationships between the viewpoints and their associated outputs, preventing their use in information-gathering schemes. To fill this gap, we propose a novel attention-based architecture, trained via Reinforcement Learning (RL), that outputs the next viewpoint for the drone favoring the acquisition of evidence from as many unclassified targets as possible while reasoning about their movement, orientation, and occlusions. Then, we use a low-level MPC controller to move the drone to the desired viewpoint taking into account its actual dynamics. We show that our approach not only outperforms a variety of baselines but also generalizes to scenarios unseen during training. Additionally, we show that the network scales to large numbers of targets and generalizes well to different movement dynamics of the targets.

Moritz A. Zanger, Yijun Wu, Pascal R. Van der Vaart et al.

Uncertainty quantification is central to safe and efficient deployments of deep learning models, yet many computationally practical methods lack lacking rigorous theoretical motivation. Random network distillation (RND) is a lightweight technique that measures novelty via prediction errors against a fixed random target. While empirically effective, it has remained unclear what uncertainties RND measures and how its estimates relate to other approaches, e.g. Bayesian inference or deep ensembles. This paper establishes these missing theoretical connections by analyzing RND within the neural tangent kernel framework in the limit of infinite network width. Our analysis reveals two central findings in this limit: (1) The uncertainty signal from RND -- its squared self-predictive error -- is equivalent to the predictive variance of a deep ensemble. (2) By constructing a specific RND target function, we show that the RND error distribution can be made to mirror the centered posterior predictive distribution of Bayesian inference with wide neural networks. Based on this equivalence, we moreover devise a posterior sampling algorithm that generates i.i.d. samples from an exact Bayesian posterior predictive distribution using this modified \textit{Bayesian RND} model. Collectively, our findings provide a unified theoretical perspective that places RND within the principled frameworks of deep ensembles and Bayesian inference, and offer new avenues for efficient yet theoretically grounded uncertainty quantification methods.

Caroline Horsch, Laurens Engwegen, Max Weltevrede et al.

In reinforcement learning, abstraction methods that remove unnecessary information from the observation are commonly used to learn policies which generalize better to unseen tasks. However, these methods often overlook a crucial weakness: the function which extracts the reduced-information representation has unknown generalization ability in unseen observations. In this paper, we address this problem by presenting an information removal method which more reliably generalizes to new states. We accomplish this by using a learned masking function which operates on, and is integrated with, the attention weights within an attention-based policy network. We demonstrate that our method significantly improves policy generalization to unseen tasks in the Procgen benchmark compared to standard PPO and masking approaches.

Grigorii Veviurko, Wendelin Böhmer, Mathijs de Weerdt

In reinforcement learning (RL), different reward functions can define the same optimal policy but result in drastically different learning performance. For some, the agent gets stuck with a suboptimal behavior, and for others, it solves the task efficiently. Choosing a good reward function is hence an extremely important yet challenging problem. In this paper, we explore an alternative approach for using rewards for learning. We introduce \textit{max-reward RL}, where an agent optimizes the maximum rather than the cumulative reward. Unlike earlier works, our approach works for deterministic and stochastic environments and can be easily combined with state-of-the-art RL algorithms. In the experiments, we study the performance of max-reward RL algorithms in two goal-reaching environments from Gymnasium-Robotics and demonstrate its benefits over standard RL. The code is available at https://github.com/veviurko/To-the-Max.

Yaniv Oren, Viliam Vadocz, Joery A. de Vries et al.

Monte Carlo Tree Search (MCTS) is a widely used approach for policy improvement through search with increasing popularity for real world applications. Due to the sequential and deterministic nature of its search, runtime-scaling of MCTS with parallel compute remains a major challenge. We introduce Particle MCTS (PMCTS), to our knowledge the first principled parallel MCTS algorithm which is suited for neural network evaluations and can preserve formal policy improvement guarantees. Empirically, PMCTS scales well with parallel compute and significantly outperforms the popular heuristic-based baselines across domains.

Moritz A. Zanger, Pascal R. Van der Vaart, Wendelin Böhmer et al.

Uncertainty quantification is a critical aspect of reinforcement learning and deep learning, with numerous applications ranging from efficient exploration and stable offline reinforcement learning to outlier detection in medical diagnostics. The scale of modern neural networks, however, complicates the use of many theoretically well-motivated approaches such as full Bayesian inference. Approximate methods like deep ensembles can provide reliable uncertainty estimates but still remain computationally expensive. In this work, we propose contextual similarity distillation, a novel approach that explicitly estimates the variance of an ensemble of deep neural networks with a single model, without ever learning or evaluating such an ensemble in the first place. Our method builds on the predictable learning dynamics of wide neural networks, governed by the neural tangent kernel, to derive an efficient approximation of the predictive variance of an infinite ensemble. Specifically, we reinterpret the computation of ensemble variance as a supervised regression problem with kernel similarities as regression targets. The resulting model can estimate predictive variance at inference time with a single forward pass, and can make use of unlabeled target-domain data or data augmentations to refine its uncertainty estimates. We empirically validate our method across a variety of out-of-distribution detection benchmarks and sparse-reward reinforcement learning environments. We find that our single-model method performs competitively and sometimes superior to ensemble-based baselines and serves as a reliable signal for efficient exploration. These results, we believe, position contextual similarity distillation as a principled and scalable alternative for uncertainty quantification in reinforcement learning and general deep learning.

Ksenija Stepanovic, Wendelin Böhmer, Mathijs de Weerdt

Traditional mathematical programming solvers require long computational times to solve constrained minimization problems of complex and large-scale physical systems. Therefore, these problems are often transformed into unconstrained ones, and solved with computationally efficient optimization approaches based on first-order information, such as the gradient descent method. However, for unconstrained problems, balancing the minimization of the objective function with the reduction of constraint violations is challenging. We consider the class of time-dependent minimization problems with increasing (possibly) nonlinear and non-convex objective function and non-decreasing (possibly) nonlinear and non-convex inequality constraints. To efficiently solve them, we propose a penalty-based guardrail algorithm (PGA). This algorithm adapts a standard penalty-based method by dynamically updating the right-hand side of the constraints with a guardrail variable which adds a margin to prevent violations. We evaluate PGA on two novel application domains: a simplified model of a district heating system and an optimization model derived from learned deep neural networks. Our method significantly outperforms mathematical programming solvers and the standard penalty-based method, and achieves better performance and faster convergence than a state-of-the-art algorithm (IPDD) within a specified time limit.

Yaniv Oren, Joery A. de Vries, Pascal R. van der Vaart et al.

Model-based reinforcement learning (RL) methods that leverage search are responsible for many milestone breakthroughs in RL. Sequential Monte Carlo (SMC) recently emerged as an alternative to the Monte Carlo Tree Search (MCTS) algorithm which drove these breakthroughs. SMC is easier to parallelize and more suitable to GPU acceleration. However, it also suffers from large variance and path degeneracy which prevent it from scaling well with increased search depth, i.e., increased sequential compute. To address these problems, we introduce Twice Sequential Monte Carlo Tree Search (TSMCTS). Across discrete and continuous environments TSMCTS outperforms the SMC baseline as well as a popular modern version of MCTS. Through variance reduction and mitigation of path degeneracy, TSMCTS scales favorably with sequential compute while retaining the properties that make SMC natural to parallelize.

Emil Malmsten, Wendelin Böhmer

We present TransZero, a model-based reinforcement learning algorithm that removes the sequential bottleneck in Monte Carlo Tree Search (MCTS). Unlike MuZero, which constructs its search tree step by step using a recurrent dynamics model, TransZero employs a transformer-based network to generate multiple latent future states simultaneously. Combined with the Mean-Variance Constrained (MVC) evaluator that eliminates dependence on inherently sequential visitation counts, our approach enables the parallel expansion of entire subtrees during planning. Experiments in MiniGrid and LunarLander show that TransZero achieves up to an eleven-fold speedup in wall-clock time compared to MuZero while maintaining sample efficiency. These results demonstrate that parallel tree construction can substantially accelerate model-based reinforcement learning, bringing real-time decision-making in complex environments closer to practice. The code is publicly available on GitHub.

Isidoro Tamassia, Wendelin Böhmer

The AlphaZero framework provides a standard way of combining Monte Carlo planning with prior knowledge provided by a previously trained policy-value neural network. AlphaZero usually assumes that the environment on which the neural network was trained will not change at test time, which constrains its applicability. In this paper, we analyze the problem of deploying AlphaZero agents in potentially changed test environments and demonstrate how the combination of simple modifications to the standard framework can significantly boost performance, even in settings with a low planning budget available. The code is publicly available on GitHub.

Laurens Engwegen, Daan Brinks, Wendelin Böhmer

A universal controller for any robot morphology would greatly improve computational and data efficiency. By utilizing contextual information about the properties of individual robots and exploiting their modular structure in the architecture of deep reinforcement learning agents, steps have been made towards multi-robot control. Generalization to new, unseen robots, however, remains a challenge. In this paper we hypothesize that the relevant contextual information is partially observable, but that it can be inferred through interactions for better generalization to contexts that are not seen during training. To this extent, we implement a modular recurrent architecture and evaluate its generalization performance on a large set of MuJoCo robots. The results show a substantial improved performance on robots with unseen dynamics, kinematics, and topologies, in four different environments.

Moritz A. Zanger, Max Weltevrede, Yaniv Oren et al.

Estimating epistemic uncertainty in value functions is a crucial challenge for many aspects of reinforcement learning (RL), including efficient exploration, safe decision-making, and offline RL. While deep ensembles provide a robust method for quantifying value uncertainty, they come with significant computational overhead. Single-model methods, while computationally favorable, often rely on heuristics and typically require additional propagation mechanisms for myopic uncertainty estimates. In this work we introduce universal value-function uncertainties (UVU), which, similar in spirit to random network distillation (RND), quantify uncertainty as squared prediction errors between an online learner and a fixed, randomly initialized target network. Unlike RND, UVU errors reflect policy-conditional value uncertainty, incorporating the future uncertainties any given policy may encounter. This is due to the training procedure employed in UVU: the online network is trained using temporal difference learning with a synthetic reward derived from the fixed, randomly initialized target network. We provide an extensive theoretical analysis of our approach using neural tangent kernel (NTK) theory and show that in the limit of infinite network width, UVU errors are exactly equivalent to the variance of an ensemble of independent universal value functions. Empirically, we show that UVU achieves equal performance to large ensembles on challenging multi-task offline RL settings, while offering simplicity and substantial computational savings.

Max Weltevrede, Moritz A. Zanger, Matthijs T. J. Spaan et al.

In the zero-shot policy transfer setting in reinforcement learning, the goal is to train an agent on a fixed set of training environments so that it can generalise to similar, but unseen, testing environments. Previous work has shown that policy distillation after training can sometimes produce a policy that outperforms the original in the testing environments. However, it is not yet entirely clear why that is, or what data should be used to distil the policy. In this paper, we prove, under certain assumptions, a generalisation bound for policy distillation after training. The theory provides two practical insights: for improved generalisation, you should 1) train an ensemble of distilled policies, and 2) distil it on as much data from the training environments as possible. We empirically verify that these insights hold in more general settings, when the assumptions required for the theory no longer hold. Finally, we demonstrate that an ensemble of policies distilled on a diverse dataset can generalise significantly better than the original agent.

Saray Bakker, Rodrigo Pérez-Dattari, Cosimo Della Santina et al.

Using the language of dynamical systems, Imitation learning (IL) provides an intuitive and effective way of teaching stable task-space motions to robots with goal convergence. Yet, IL techniques are affected by serious limitations when it comes to ensuring safety and fulfillment of physical constraints. With this work, we solve this challenge via TamedPUMA, an IL algorithm augmented with a recent development in motion generation called geometric fabrics. As both the IL policy and geometric fabrics describe motions as artificial second-order dynamical systems, we propose two variations where IL provides a navigation policy for geometric fabrics. The result is a stable imitation learning strategy within which we can seamlessly blend geometrical constraints like collision avoidance and joint limits. Beyond providing a theoretical analysis, we demonstrate TamedPUMA with simulated and real-world tasks, including a 7-DoF manipulator.

Laurens Engwegen, Daan Brinks, Wendelin Böhmer

Novel imaging and neurostimulation techniques open doors for advancements in closed-loop control of activity in biological neural networks. This would allow for applications in the investigation of activity propagation, and for diagnosis and treatment of pathological behaviour. Due to the partially observable characteristics of activity propagation, through networks in which edges can not be observed, and the dynamic nature of neuronal systems, there is a need for adaptive, generalisable control. In this paper, we introduce an environment that procedurally generates neuronal networks with different topologies to investigate this generalisation problem. Additionally, an existing transformer-based architecture is adjusted to evaluate the generalisation performance of a deep RL agent in the presented partially observable environment. The agent demonstrates the capability to generalise control from a limited number of training networks to unseen test networks.

Max Weltevrede, Felix Kaubek, Matthijs T. J. Spaan et al.

One of the remaining challenges in reinforcement learning is to develop agents that can generalise to novel scenarios they might encounter once deployed. This challenge is often framed in a multi-task setting where agents train on a fixed set of tasks and have to generalise to new tasks. Recent work has shown that in this setting increased exploration during training can be leveraged to increase the generalisation performance of the agent. This makes sense when the states encountered during testing can actually be explored during training. In this paper, we provide intuition why exploration can also benefit generalisation to states that cannot be explicitly encountered during training. Additionally, we propose a novel method Explore-Go that exploits this intuition by increasing the number of states on which the agent trains. Explore-Go effectively increases the starting state distribution of the agent and as a result can be used in conjunction with most existing on-policy or off-policy reinforcement learning algorithms. We show empirically that our method can increase generalisation performance in an illustrative environment and on the Procgen benchmark.

Tarun Gupta, Anuj Mahajan, Bei Peng et al.

VDN and QMIX are two popular value-based algorithms for cooperative MARL that learn a centralized action value function as a monotonic mixing of per-agent utilities. While this enables easy decentralization of the learned policy, the restricted joint action value function can prevent them from solving tasks that require significant coordination between agents at a given timestep. We show that this problem can be overcome by improving the joint exploration of all agents during training. Specifically, we propose a novel MARL approach called Universal Value Exploration (UneVEn) that learns a set of related tasks simultaneously with a linear decomposition of universal successor features. With the policies of already solved related tasks, the joint exploration process of all agents can be improved to help them achieve better coordination. Empirical results on a set of exploration games, challenging cooperative predator-prey tasks requiring significant coordination among agents, and StarCraft II micromanagement benchmarks show that UneVEn can solve tasks where other state-of-the-art MARL methods fail.

Shariq Iqbal, Christian A. Schroeder de Witt, Bei Peng et al.

Multi-agent settings in the real world often involve tasks with varying types and quantities of agents and non-agent entities; however, common patterns of behavior often emerge among these agents/entities. Our method aims to leverage these commonalities by asking the question: ``What is the expected utility of each agent when only considering a randomly selected sub-group of its observed entities?'' By posing this counterfactual question, we can recognize state-action trajectories within sub-groups of entities that we may have encountered in another task and use what we learned in that task to inform our prediction in the current one. We then reconstruct a prediction of the full returns as a combination of factors considering these disjoint groups of entities and train this ``randomly factorized" value function as an auxiliary objective for value-based multi-agent reinforcement learning. By doing so, our model can recognize and leverage similarities across tasks to improve learning efficiency in a multi-task setting. Our approach, Randomized Entity-wise Factorization for Imagined Learning (REFIL), outperforms all strong baselines by a significant margin in challenging multi-task StarCraft micromanagement settings.

Bei Peng, Tabish Rashid, Christian A. Schroeder de Witt et al.

We propose FACtored Multi-Agent Centralised policy gradients (FACMAC), a new method for cooperative multi-agent reinforcement learning in both discrete and continuous action spaces. Like MADDPG, a popular multi-agent actor-critic method, our approach uses deep deterministic policy gradients to learn policies. However, FACMAC learns a centralised but factored critic, which combines per-agent utilities into the joint action-value function via a non-linear monotonic function, as in QMIX, a popular multi-agent Q-learning algorithm. However, unlike QMIX, there are no inherent constraints on factoring the critic. We thus also employ a nonmonotonic factorisation and empirically demonstrate that its increased representational capacity allows it to solve some tasks that cannot be solved with monolithic, or monotonically factored critics. In addition, FACMAC uses a centralised policy gradient estimator that optimises over the entire joint action space, rather than optimising over each agent's action space separately as in MADDPG. This allows for more coordinated policy changes and fully reaps the benefits of a centralised critic. We evaluate FACMAC on variants of the multi-agent particle environments, a novel multi-agent MuJoCo benchmark, and a challenging set of StarCraft II micromanagement tasks. Empirical results demonstrate FACMAC's superior performance over MADDPG and other baselines on all three domains.

Tabish Rashid, Bei Peng, Wendelin Böhmer et al.

Optimistic initialisation is an effective strategy for efficient exploration in reinforcement learning (RL). In the tabular case, all provably efficient model-free algorithms rely on it. However, model-free deep RL algorithms do not use optimistic initialisation despite taking inspiration from these provably efficient tabular algorithms. In particular, in scenarios with only positive rewards, Q-values are initialised at their lowest possible values due to commonly used network initialisation schemes, a pessimistic initialisation. Merely initialising the network to output optimistic Q-values is not enough, since we cannot ensure that they remain optimistic for novel state-action pairs, which is crucial for exploration. We propose a simple count-based augmentation to pessimistically initialised Q-values that separates the source of optimism from the neural network. We show that this scheme is provably efficient in the tabular setting and extend it to the deep RL setting. Our algorithm, Optimistic Pessimistically Initialised Q-Learning (OPIQ), augments the Q-value estimates of a DQN-based agent with count-derived bonuses to ensure optimism during both action selection and bootstrapping. We show that OPIQ outperforms non-optimistic DQN variants that utilise a pseudocount-based intrinsic motivation in hard exploration tasks, and that it predicts optimistic estimates for novel state-action pairs.

Wendelin Böhmer, Vitaly Kurin, Shimon Whiteson

This paper introduces the deep coordination graph (DCG) for collaborative multi-agent reinforcement learning. DCG strikes a flexible trade-off between representational capacity and generalization by factoring the joint value function of all agents according to a coordination graph into payoffs between pairs of agents. The value can be maximized by local message passing along the graph, which allows training of the value function end-to-end with Q-learning. Payoff functions are approximated with deep neural networks that employ parameter sharing and low-rank approximations to significantly improve sample efficiency. We show that DCG can solve predator-prey tasks that highlight the relative overgeneralization pathology, as well as challenging StarCraft II micromanagement tasks.

Wendelin Böhmer, Tabish Rashid, Shimon Whiteson

This paper investigates the use of intrinsic reward to guide exploration in multi-agent reinforcement learning. We discuss the challenges in applying intrinsic reward to multiple collaborative agents and demonstrate how unreliable reward can prevent decentralized agents from learning the optimal policy. We address this problem with a novel framework, Independent Centrally-assisted Q-learning (ICQL), in which decentralized agents share control and an experience replay buffer with a centralized agent. Only the centralized agent is intrinsically rewarded, but the decentralized agents still benefit from improved exploration, without the distraction of unreliable incentives.

Maximilian Igl, Andrew Gambardella, Jinke He et al.

We present Multitask Soft Option Learning(MSOL), a hierarchical multitask framework based on Planning as Inference. MSOL extends the concept of options, using separate variational posteriors for each task, regularized by a shared prior. This ''soft'' version of options avoids several instabilities during training in a multitask setting, and provides a natural way to learn both intra-option policies and their terminations. Furthermore, it allows fine-tuning of options for new tasks without forgetting their learned policies, leading to faster training without reducing the expressiveness of the hierarchical policy. We demonstrate empirically that MSOL significantly outperforms both hierarchical and flat transfer-learning baselines.

Wendelin Böhmer, Rong Guo, Klaus Obermayer

This paper investigates a type of instability that is linked to the greedy policy improvement in approximated reinforcement learning. We show empirically that non-deterministic policy improvement can stabilize methods like LSPI by controlling the improvements' stochasticity. Additionally we show that a suitable representation of the value function also stabilizes the solution to some degree. The presented approach is simple and should also be easily transferable to more sophisticated algorithms like deep reinforcement learning.

Wendelin Böhmer, Klaus Obermayer

Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties that allow to analytically solve certain integrals and to calculate point-wise products. Applications like belief propagation and reinforcement learning can exploit these properties to break the curse and speed up computation. We derive a regularized greedy optimization scheme, that learns factored basis functions during training. The novel regression algorithm performs competitively to Gaussian processes on benchmark tasks, and the learned LFF functions are with 4-9 factored basis functions on average very compact.

Wendelin Böhmer

The application of reinforcement learning algorithms onto real life problems always bears the challenge of filtering the environmental state out of raw sensor readings. While most approaches use heuristics, biology suggests that there must exist an unsupervised method to construct such filters automatically. Besides the extraction of environmental states, the filters have to represent them in a fashion that support modern reinforcement algorithms. Many popular algorithms use a linear architecture, so one should aim at filters that have good approximation properties in combination with linear functions. This thesis wants to propose the unsupervised method slow feature analysis (SFA) for this task. Presented with a random sequence of sensor readings, SFA learns a set of filters. With growing model complexity and training examples, the filters converge against trigonometric polynomial functions. These are known to possess excellent approximation capabilities and should therfore support the reinforcement algorithms well. We evaluate this claim on a robot. The task is to learn a navigational control in a simple environment using the least square policy iteration (LSPI) algorithm. The only accessible sensor is a head mounted video camera, but without meaningful filtering, video images are not suited as LSPI input. We will show that filters learned by SFA, based on a random walk video of the robot, allow the learned control to navigate successfully in ca. 80% of the test trials.