Spatio-temporal credit assignment in population learning

Learning by reinforcement is important in shaping animal behavior, and in particular in behavioral decision making. Such decision making is likely to involve the integration of many synaptic events in space and time. However, using a single reinforcement signal to modulate synaptic plasticity, as suggested in classical reinforcement learning algorithms, a twofold problem arises. Different synapses will have contributed differently to the behavioral decision, and even for one and the same synapse, releases at different times may have had different effects. Here we present a plasticity rule which solves this spatio-temporal credit assignment problem in a population of spiking neurons. The learning rule is spike-time dependent and maximizes the expected reward by following its stochastic gradient. Synaptic plasticity is modulated not only by the reward, but also by a population feedback signal. While this additional signal solves the spatial component of the problem, the temporal one is solved by means of synaptic eligibility traces. In contrast to temporal difference (TD) based approaches to reinforcement learning, our rule is explicit with regard to the assumed biophysical mechanisms. Neurotransmitter concentrations determine plasticity and learning occurs fully online. Further, it works even if the task to be learned is non-Markovian, i.e. when reinforcement is not determined by the current state of the system but may also depend on past events. The performance of the model is assessed by studying three non-Markovian tasks. In the first task, the reward is delayed beyond the last action with non-related stimuli and actions appearing in between. The second task involves an action sequence which is itself extended in time and reward is only delivered at the last action, as it is the case in any type of board-game. The third task is the inspection game that has been studied in neuroeconomics, where an inspector tries to prevent a worker from shirking. Applying our algorithm to this game yields a learning behavior which is consistent with behavioral data from humans and monkeys, revealing themselves properties of a mixed Nash equilibrium. The examples show that our neuronal implementation of reward based learning copes with delayed and stochastic reward delivery, and also with the learning of mixed strategies in two-opponent games.

Spatio-temporal credit assignment in population learning

Learning by reinforcement is important in shaping animal behavior. But behavioral decision making is likely to involve the integration of many synaptic events in space and time. So in using a single reinforcement signal to modulate synaptic plasticity a twofold problem arises. Different synapses will have contributed differently to the behavioral decision and, even for one and the same synapse, releases at different times may have had different effects. Here we present a plasticity rule which solves this spatio-temporal credit assignment problem in a population of spiking neurons. The learning rule is spike time dependent and maximizes the expected reward by following its stochastic gradient. Synaptic plasticity is modulated not only by the reward but by a population feedback signal as well. While this additional signal solves the spatial component of the problem, the temporal one is solved by means of synaptic eligibility traces. In contrast to temporal difference based approaches to reinforcement learning, our rule is explicit with regard to the assumed biophysical mechanisms. Neurotransmitter concentrations determine plasticity and learning occurs fully online. Further, it works even if the task to be learned is non-Markovian, i.e. when reinforcement is not determined by the current state of the system but may also depend on past events. The performance of the model is assessed by studying three non-Markovian tasks. In the first task the reward is delayed beyond the last action with non-related stimuli and actions appearing in between. The second one involves an action sequence which is itself extended in time and reward is only delivered at the last action, as is the case in any type of board-game. The third is the inspection game that has been studied in neuroeconomics. It only has a mixed Nash equilibrium and exemplifies that the model also copes with stochastic reward delivery and the learning of mixed strategies.

Spatio-temporal credit assignment in population learning

We present a model for plasticity induction in reinforcement learning which is based on a cascade of synaptic memory traces. In the cascade of these so called eligibility traces presynaptic input is first corre lated with postsynaptic events, next with the behavioral decisions and finally with the external reinforcement. A population of leaky integrate and fire neurons endowed with this plasticity scheme is studied by simulation on different tasks. For operant co nditioning with delayed reinforcement, learning succeeds even when the delay is so large that the delivered reward reflects the appropriateness, not of the immediately preceeding response, but of a decision made earlier on in the stimulus - decision sequence . So the proposed model does not rely on the temporal contiguity between decision and pertinent reward and thus provides a viable means of addressing the temporal credit assignment problem. In the same task, learning speeds up with increasing population si ze, showing that the plasticity cascade simultaneously addresses the spatial problem of assigning credit to the different population neurons. Simulations on other task such as sequential decision making serve to highlight the robustness of the proposed sch eme and, further, contrast its performance to that of temporal difference based approaches to reinforcement learning.

Spatio-Temporal Credit Assignment in Neuronal Population Learning

n learning from trial and error, animals need to relate behavioral decisions to environmental reinforcement even though it may be difficult to assign credit to a particular decision when outcomes are uncertain or subject to delays. When considering the biophysical basis of learning, the credit-assignment problem is compounded because the behavioral decisions themselves result from the spatio-temporal aggregation of many synaptic releases. We present a model of plasticity induction for reinforcement learning in a population of leaky integrate and fire neurons which is based on a cascade of synaptic memory traces. Each synaptic cascade correlates presynaptic input first with postsynaptic events, next with the behavioral decisions and finally with external reinforcement. For operant conditioning, learning succeeds even when reinforcement is delivered with a delay so large that temporal contiguity between decision and pertinent reward is lost due to intervening decisions which are themselves subject to delayed reinforcement. This shows that the model provides a viable mechanism for temporal credit assignment. Further, learning speeds up with increasing population size, so the plasticity cascade simultaneously addresses the spatial problem of assigning credit to synapses in different population neurons. Simulations on other tasks, such as sequential decision making, serve to contrast the performance of the proposed scheme to that of temporal difference-based learning. We argue that, due to their comparative robustness, synaptic plasticity cascades are attractive basic models of reinforcement learning in the brain.

Allocentric and egocentric spatial impairments in a case of topographical disorientation

We describe a patient with a topographical disorientation after a stroke of the right mediotemporooccipital lobe including the parahippocampal cortex (PHC). Clinical observations and neuropsychological testing reveal an impairment of allocentric spatial representations as well as impairments of visuospatial learning and memory. These findings are in accordance with the well-known function of the PHC in topographical disorientation. As a new finding, results from oculomotor tasks show additional impairments of the egocentric spatial coordinate frame suggesting that in topographical disorientation due to a lesion of the right mediotemporooccipital lobe not only allocentric but also egocentric visuospatial functions are disturbed.

Probabilistic contingency learning with limbic or prefrontal damage

AB A fundamental capacity of the human brain is to learn relations (contingencies) between environmental stimuli and the consequences of their occurrence. Some contingencies are probabilistic; that is, they predict an event in some situations but not in all. Animal studies suggest that damage to limbic structures or the prefrontal cortex may disturb probabilistic learning. The authors studied the learning of probabilistic contingencies in amnesic patients with limbic lesions, patients with prefrontal cortex damage, and healthy controls. Across 120 trials, participants learned contingent relations between spatial sequences and a button press. Amnesic patients had learning comparable to that of control subjects but failed to indicate what they had learned. Across the last 60 trials, amnesic patients and control subjects learned to avoid a noncontingent choice better than frontal patients. These results indicate that probabilistic learning does not depend on the brain structures supporting declarative memory.

The mood-stabilizer lithium prevents hippocampal apoptosis and improves spatial memory in experimental meningitis.

Pneumococcal meningitis is associated with high morbidity and mortality rates. Brain damage caused by this disease is characterized by apoptosis in the hippocampal dentate gyrus, a morphological correlate of learning deficits in experimental paradigms. The mood stabilizer lithium has previously been found to attenuate brain damage in ischemic and inflammatory diseases of the brain. An infant rat model of pneumococcal meningitis was used to investigate the neuroprotective and neuroregenerative potential of lithium. To assess an effect on the acute disease, LiCl was administered starting five days prior to intracisternal infection with live Streptococcus pneumoniae. Clinical parameters were recorded, cerebrospinal fluid (CSF) was sampled, and the animals were sacrificed 42 hours after infection to harvest the brain and serum. Cryosections of the brains were stained for Nissl substance to quantify brain injury. Hippocampal gene expression of Bcl-2, Bax, p53, and BDNF was analyzed. Lithium concentrations were measured in serum and CSF. The effect of chronic lithium treatment on spatial memory function and cell survival in the dentate gyrus was evaluated in a Morris water maze and by quantification of BrdU incorporation after LiCl treatment during 3 weeks following infection. In the hippocampus, LiCl significantly reduced apoptosis and gene expression of Bax and p53 while it increased expression of Bcl-2. IL-10, MCP-1, and TNF were significantly increased in animals treated with LiCl compared to NaCl. Chronic LiCl treatment improved spatial memory in infected animals. The mood stabilizer lithium may thus be a therapeutic alternative to attenuate neurofunctional deficits as a result of pneumococcal meningitis.