Biological learning operates at multiple interlocking timescales, from long evolutionary stretches down to the relatively short time span of an individual's life. While each process has been simulated individually as a basic learning algorithm in the context of spiking neuronal networks (SNNs), the integration of the two has remained limited. In this study, we first train SNNs separately using individual model learning using spike-timing dependent reinforcement learning (STDP-RL) and evolutionary (EVOL) learning algorithms to solve the CartPole reinforcement learning (RL) control problem. We then develop an interleaved algorithm inspired by biological evolution that combines the EVOL and STDP-RL learning in sequence. We use the NEURON simulator with NetPyNE to create an SNN interfaced with the CartPole environment from OpenAI's Gym. In CartPole, the goal is to balance a vertical pole by moving left/right on a 1-D plane. Our SNN contains multiple populations of neurons organized in three layers: sensory layer, association/hidden layer, and motor layer, where neurons are connected by excitatory (AMPA/NMDA) and inhibitory (GABA) synapses. Association and motor layers contain one excitatory (E) population and two inhibitory (I) populations with different synaptic time constants. Each neuron is an event-based integrate-and-fire model with plastic connections between excitatory neurons. In our SNN, the environment activates sensory neurons tuned to specific features of the game state. We split the motor population into subsets representing each movement choice. The subset with more spiking over an interval determines the action. During STDP-RL, we supply intermediary evaluations (reward/punishment) of each action by judging the effectiveness of a move (e.g., moving the CartPole to a balanced position). During EVOL, updates consist of adding together many random perturbations of the connection weights. Each set of random perturbations is weighted by the total episodic reward it achieves when applied independently. We evaluate the performance of each algorithm after training and through the creation of sensory/motor action maps that delineate the network's transformation of sensory inputs into higher-order representations and eventual motor decisions. Both EVOL and STDP-RL training produce SNNs capable of moving the cart left and right and keeping the pole vertical. Compared to the STDP-RL and EVOL algorithms operating on their own, our interleaved training paradigm produced enhanced robustness in performance, with different strategies revealed through analysis of the sensory/motor mappings. Analysis of synaptic weight matrices also shows distributed vs clustered representations after the EVOL and STDP-RL algorithms, respectively. These weight differences also manifest as diffuse vs synchronized firing patterns. Our modeling opens up new capabilities for SNNs in RL and could serve as a testbed for neurobiologists aiming to understand multi-timescale learning mechanisms and dynamics in neuronal circuits.
Quenched Decay of Correlations for One-dimensional Random Lorenz Maps
