Reinforcement Learning
Stress, noradrenaline, and realistic prediction of mouse behaviour using reinforcement learning
Sandi, Carmen, Gerstner, Wulfram, Lukšys, Gediminas
Suppose we train an animal in a conditioning experiment. Can one predict how a given animal, under given experimental conditions, would perform the task? Since various factors such as stress, motivation, genetic background, and previous errors in task performance can influence animal behaviour, this appears to be a very challenging aim. Reinforcement learning (RL) models have been successful in modeling animal (and human) behaviour, but their success has been limited because of uncertainty as to how to set meta-parameters (such as learning rate, exploitation-exploration balance and future reward discount factor) that strongly influence model performance. We show that a simple RL model whose metaparameters are controlled by an artificial neural network, fed with inputs such as stress, affective phenotype, previous task performance, and even neuromodulatory manipulations, can successfully predict mouse behaviour in the "hole-box" - a simple conditioning task. Our results also provide important insights on how stress and anxiety affect animal learning, performance accuracy, and discounting of future rewards, and on how noradrenergic systems can interact with these processes.
Psychiatry: Insights into depression through normative decision-making models
Huys, Quentin J., Vogelstein, Joshua, Dayan, Peter
Decision making lies at the very heart of many psychiatric diseases. It is also a central theoretical concern in a wide variety of fields and has undergone detailed, in-depth, analyses. We take as an example Major Depressive Disorder (MDD), applying insights from a Bayesian reinforcement learning framework. We focus on anhedonia and helplessness. Helplessness--a core element in the conceptualizations ofMDD that has lead to major advances in its treatment, pharmacological and neurobiological understanding--is formalized as a simple prior over the outcome entropy of actions in uncertain environments.
Convergent Temporal-Difference Learning with Arbitrary Smooth Function Approximation
Bhatnagar, Shalabh, Precup, Doina, Silver, David, Sutton, Richard S., Maei, Hamid R., Szepesvári, Csaba
We introduce the first temporal-difference learning algorithms that converge with smooth value function approximators, such as neural networks. Conventional temporal-difference (TD) methods, such as TD($\lambda$), Q-learning and Sarsa have been used successfully with function approximation in many applications. However, it is well known that off-policy sampling, as well as nonlinear function approximation, can cause these algorithms to become unstable (i.e., the parameters of the approximator may diverge). Sutton et al (2009a,b) solved the problem of off-policy learning with linear TD algorithms by introducing a new objective function, related to the Bellman-error, and algorithms that perform stochastic gradient-descent on this function. In this paper, we generalize their work to nonlinear function approximation. We present a Bellman error objective function and two gradient-descent TD algorithms that optimize it. We prove the asymptotic almost-sure convergence of both algorithms for any finite Markov decision process and any smooth value function approximator, under usual stochastic approximation conditions. The computational complexity per iteration scales linearly with the number of parameters of the approximator. The algorithms are incremental and are guaranteed to converge to locally optimal solutions.
A computational model of hippocampal function in trace conditioning
Ludvig, Elliot A., Sutton, Richard S., Verbeek, Eric, Kehoe, E. J.
We present a new reinforcement-learning model for the role of the hippocampus in classical conditioning, focusing on the differences between trace and delay conditioning. In the model, all stimuli are represented both as unindividuated wholes and as a series of temporal elements with varying delays. These two stimulus representations interact, producing different patterns of learning in trace and delay conditioning. The model proposes that hippocampal lesions eliminate long-latency temporal elements, but preserve short-latency temporal elements. For trace conditioning, with no contiguity between stimulus and reward, these long-latency temporal elements are vital to learning adaptively timed responses. For delay conditioning, in contrast, the continued presence of the stimulus supports conditioned responding, and the short-latency elements suppress responding early in the stimulus. In accord with the empirical data, simulated hippocampal damage impairs trace conditioning, but not delay conditioning, at medium-length intervals. With longer intervals, learning is impaired in both procedures, and, with shorter intervals, in neither. In addition, the model makes novel predictions about the response topography with extended stimuli or post-training lesions. These results demonstrate how temporal contiguity, as in delay conditioning, changes the timing problem faced by animals, rendering it both easier and less susceptible to disruption by hippocampal lesions.
Learning to Use Working Memory in Partially Observable Environments through Dopaminergic Reinforcement
Todd, Michael T., Niv, Yael, Cohen, Jonathan D.
Working memory is a central topic of cognitive neuroscience because it is critical for solving real world problems in which information from multiple temporally distant sources must be combined to generate appropriate behavior. However, an often neglected fact is that learning to use working memory effectively is itself a difficult problem. The Gating" framework is a collection of psychological models that show how dopamine can train the basal ganglia and prefrontal cortex to form useful working memory representations in certain types of problems. We bring together gating with ideas from machine learning about using finite memory systems in more general problems. Thus we present a normative Gating model that learns, by online temporal difference methods, to use working memory to maximize discounted future rewards in general partially observable settings. The model successfully solves a benchmark working memory problem, and exhibits limitations similar to those observed in human experiments. Moreover, the model introduces a concise, normative definition of high level cognitive concepts such as working memory and cognitive control in terms of maximizing discounted future rewards."
On the asymptotic equivalence between differential Hebbian and temporal difference learning using a local third factor
Kolodziejski, Christoph, Porr, Bernd, Tamosiunaite, Minija, Wörgötter, Florentin
In this theoretical contribution we provide mathematical proof that two of the most important classes of network learning - correlation-based differential Hebbian learningand reward-based temporal difference learning - are asymptotically equivalent when timing the learning with a local modulatory signal. This opens the opportunity to consistently reformulate most of the abstract reinforcement learning frameworkfrom a correlation based perspective that is more closely related to the biophysics of neurons.
Training Factor Graphs with Reinforcement Learning for Efficient MAP Inference
Rohanimanesh, Khashayar, Singh, Sameer, McCallum, Andrew, Black, Michael J.
Large, relational factor graphs with structure defined by first-order logic or other languages give rise to notoriously difficult inference problems. Because unrolling the structure necessary to represent distributions over all hypotheses has exponential blow-up, solutions are often derived from MCMC. However, because of limitations in the design and parameterization of the jump function, these sampling-based methods suffer from local minima|the system must transition through lower-scoring configurations before arriving at a better MAP solution. This paper presents a new method of explicitly selecting fruitful downward jumps by leveraging reinforcement learning (RL). Rather than setting parameters to maximize the likelihood of the training data, parameters of the factor graph are treated as a log-linear function approximator and learned with temporal difference (TD); MAP inference is performed by executing the resulting policy on held out test data. Our method allows efficient gradient updates since only factors in the neighborhood of variables affected by an action need to be computed|we bypass the need to compute marginals entirely. Our method provides dramatic empirical success, producing new state-of-the-art results on a complex joint model of ontology alignment, with a 48\% reduction in error over state-of-the-art in that domain.
Biasing Approximate Dynamic Programming with a Lower Discount Factor
Petrik, Marek, Scherrer, Bruno
Most algorithms for solving Markov decision processes rely on a discount factor, which ensures their convergence. It is generally assumed that using an artificially low discount factor will improve the convergence rate, while sacrificing the solution quality.We however demonstrate that using an artificially low discount factor may significantly improve the solution quality, when used in approximate dynamic programming. We propose two explanations of this phenomenon. The first justification followsdirectly from the standard approximation error bounds: using a lower discount factor may decrease the approximation error bounds. However, we also show that these bounds are loose, thus their decrease does not entirely justify the improved solution quality. We thus propose another justification: when the rewards are received only sporadically (as in the case of Tetris), we can derive tighter bounds, which support a significant improvement in the solution quality with a decreased discount factor.
Temporal Difference Based Actor Critic Learning - Convergence and Neural Implementation
Castro, Dotan D., Volkinshtein, Dmitry, Meir, Ron
Actor-critic algorithms for reinforcement learning are achieving renewed popularity dueto their good convergence properties in situations where other approaches often fail (e.g., when function approximation is involved). Interestingly, there is growing evidence that actor-critic approaches based on phasic dopamine signals play a key role in biological learning through cortical and basal ganglia loops. We derive a temporal difference based actor critic learning algorithm, for which convergence can be proved without assuming widely separated time scales for the actor and the critic. The approach is demonstrated by applying it to networks of spiking neurons. The established relation between phasic dopamine and the temporal difference signal lends support to the biological relevance of such algorithms.
Policy Search for Motor Primitives in Robotics
Many motor skills in humanoid robotics can be learned using parametrized motor primitives as done in imitation learning. However, most interesting motor learning problems are high-dimensional reinforcement learning problems often beyond the reach of current methods. In this paper, we extend previous work on policy learning from the immediate reward case to episodic reinforcement learning. We show that this results into a general, common framework also connected to policy gradient methods and yielding a novel algorithm for policy learning by assuming a form of exploration that is particularly well-suited for dynamic motor primitives. The resulting algorithm is an EM-inspired algorithm applicable in complex motor learning tasks. We compare this algorithm to alternative parametrized policy search methods and show that it outperforms previous methods. We apply it in the context of motor learning and show that it can learn a complex Ball-in-a-Cup task using a real Barrett WAM robot arm.