Brain signals of a Surprise-Actor-Critic model: Evidence for multiple learning modules in human decision making

Learning how to reach a reward over long series of actions is a remarkable capability of humans, and potentially guided by multiple parallel learning modules. Current brain imaging of learning modules is limited by (i) simple experimental paradigms, (ii) entanglement of brain signals of different learning modules, and (iii) a limited number of computational models considered as candidates for explaining behavior. Here, we address these three limitations and (i) introduce a complex sequential decision making task with surprising events that allows us to (ii) dissociate correlates of reward prediction errors from those of surprise in functional magnetic resonance imaging (fMRI); and (iii) we test behavior against a large repertoire of model-free, model-based, and hybrid reinforcement learning algorithms, including a novel surprise-modulated actor-critic algorithm. Surprise, derived from an approximate Bayesian approach for learning the world-model, is extracted in our algorithm from a state prediction error. Surprise is then used to modulate the learning rate of a model-free actor, which itself learns via the reward prediction error from model-free value estimation by the critic. We find that action choices are well explained by pure model-free policy gradient, but reaction times and neural data are not. We identify signatures of both model-free and surprise-based learning signals in blood oxygen level dependent (BOLD) responses, supporting the existence of multiple parallel learning modules in the brain. Our results extend previous fMRI findings to a multi-step setting and emphasize the role of policy gradient and surprise signalling in human learning.

Surprise-based model estimation in reinforcement learning: algorithms and brain signatures

Vasiliki Liakoni

Learning how to act and adapting to unexpected changes are remarkable capabilities of humans and other animals. In the absence of a direct recipe to follow in life, behaviour is often guided by rewarding and by surprising events. A positive or a negative outcome influences the tendency to repeat some actions, and a sudden unexpected event signals the possible need to act differently or to update one's view about the world. Advances in computational, behavioral, and cognitive neuroscience have indicated that animals employ multiple strategies to learn from interaction. However, our understanding of learning strategies and how they are combined is largely restricted. The main goal of this thesis is to study the use of surprise by ever-adapting biological agents, its contributions to reward-based learning, and its manifestation in the human brain. We first study surprise from a theoretical perspective. In a probabilistic model of changing environments, we show that exact and approximate Bayesian inference give rise to a trade-off between forgetting old observations and integrating them with new ones, modulated by a naturally emerging surprise measure. We develop novel surprised-based algorithms that can adapt in the face of abrupt changes and accurately estimate the model of the world, and that could potentially be implemented in the brain. Next, we focus on the contributions of surprise-based model estimation to reinforcement learning. We couple one of our adaptive algorithms as well as simpler non-adaptive methods with reinforcement learning agents and evaluate their performance on environments exhibiting different characteristics. Abrupt changes that directly affect the agent's policy call for surprise-based adaptation, in order to achieve higher performance. Often, however, the agent does not need to invest in maintaining an accurate model of the environment to obtain high reward levels. More specifically, in stochastic environments or in environments with distal changes, simpler methods, equipped with exploration capacity, perform equally well compared to more elaborate methods. Finally, we turn to human learning behaviour and brain signals of surprise- and reward-based learning. We design a novel sequential decision making task of multiple steps where strategic use of surprising events allows us to dissociate fMRI brain correlates of reward learning and model estimation. We show that Bayesian inference on this task leads to the same surprise measure we found earlier, where the trade-off is now between ignoring new observations and integrating them with the old belief, and we develop reinforcement learning algorithms that perform outlier detection via this surprise-modulated trade-off. At the level of behaviour we find evidence for a model-free policy learning architecture, with potential influences from a model estimation system. At the level of brain responses we identify signatures of both reward- and model estimation signals, supporting the existence of multiple parallel learning systems in the brain. This thesis presents a comparative analysis of surprise-based model estimation methods in theory and simulations, provides insights in the type of approximations that biological agents may adopt, and identifies signatures of model estimation in the human brain. Our results may aid future work aiming at building efficient adaptive agents and at understanding the learning algorithms and the surprise measures implemented in the brain.

EPFL2021

Time course of prediction errors in sequential decision making

Michael Herzog, He Xu

In reinforcement learning, an agent makes sequential decisions to maximize reward. During learning, the actual and expected outcome are compared to tell whether a decision was good or bad. The difference between the actual outcome and expected outcome is the prediction error. The prediction error can be categorised into state prediction errors (SPE) and reward prediction errors (RPE). which can serve as a teaching signal in reinforcement learning. fMRI studies revealed the brain areas where the reward prediction error and the state prediction error are computed (Haruno & Kawato 2006; McClure et al. 2003; O’Doherty et al. 2003; D’Ardenne et al. 2008; Glascher et al. 2010). Here, by using 128-channel EEG, we show when the SPE and RPE are computed. In our study, participants saw an image on the computer screen and were asked to click one out of three or four buttons, which, depending on the choice, led to the presentation of a new image until a goal image was reached. After participants have learned the path to the goal, we swapped two images. The swapped images created a SPE, which was correlated with a significant change in the frontal N1 component in the Event-Related Potential. To estimate the RPE, we fit participants’ performance to a reinforcement learning algorithm SARSA-Lambda. A time window at 200-400ms in the ERP reflected well the magnitudes of the RPEs of this algorithm (r = 0.51, p = 0.02). Our results show that the frontal P3 component in ERP reflects the reward prediction process, while the state prediction process is reflected by the frontal N1 component, which is in line with the mismatch negativity studies(Campbell et al. 2007).

2018

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

Our brain continuously self-organizes to construct and maintain an internal representation of the world based on the information arriving through sensory stimuli. Remarkably, cortical areas related to different sensory modalities appear to share the same functional unit, the neuron, and develop through the same learning mechanism, synaptic plasticity. It motivates the conjecture of a unifying theory to explain cortical representational learning across sensory modalities. In this thesis we present theories and computational models of learning and optimization in neural networks, postulating functional properties of synaptic plasticity that support the apparent universal learning capacity of cortical networks. In the past decades, a variety of theories and models have been proposed to describe receptive field formation in sensory areas. They include normative models such as sparse coding, and bottom-up models such as spike-timing dependent plasticity. We bring together candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. A surprising result is that our findings are independent of specific details, and allow for robust predictions of the learned receptive fields. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. The Hebbian learning theory substantiates that synaptic plasticity can be interpreted as an optimization procedure, implementing stochastic gradient descent. In stochastic gradient descent inputs arrive sequentially, as in sensory streams. However, individual data samples have very little information about the correct learning signal, and it becomes a fundamental problem to know how many samples are required for reliable synaptic changes. Through estimation theory, we develop a novel adaptive learning rate model, that adapts the magnitude of synaptic changes based on the statistics of the learning signal, enabling an optimal use of data samples. Our model has a simple implementation and demonstrates improved learning speed, making this a promising candidate for large artificial neural network applications. The model also makes predictions on how cortical plasticity may modulate synaptic plasticity for optimal learning. The optimal sampling size for reliable learning allows us to estimate optimal learning times for a given model. We apply this theory to derive analytical bounds on times for the optimization of synaptic connections. First, we show this optimization problem to have exponentially many saddle-nodes, which lead to small gradients and slow learning. Second, we show that the number of input synapses to a neuron modulates the magnitude of the initial gradient, determining the duration of learning. Our final result reveals that the learning duration increases supra-linearly with the number of synapses, suggesting an effective limit on synaptic connections and receptive field sizes in developing neural networks.