Every Hidden Unit Maximizing Output Weights Maximizes The Global Reward

For a network of stochastic units trained on a reinforcement learning task, one biologically plausible way of learning is to treat each unit as a reinforcement learning unit and train each unit by REINFORCE using the same global reward signal. In this case, only a global reward signal has to be broadcast to all units, and the learning rule given is local. Although this learning rule follows the gradient of return in expectation, it suffers from high variance and cannot be used to train a deep network in practice. In this paper, we propose an algorithm called Weight Maximization, which can significantly improve the speed of applying REINFORCE to all units. Essentially, we replace the global reward to each hidden unit with the change in the norm of output weights, such that each hidden unit in the network is trying to maximize the norm of output weights instead of the global reward. We found that the new algorithm can solve simple reinforcement learning tasks significantly faster than the baseline model. We also prove that the resulting learning rule is approximately following gradient ascent on the reward in expectation when applied to a multi-layer network of Bernoulli logistic unit. It illustrates an example of intelligent behavior arising from a population of self-interested hedonistic neurons, which corresponds to Klopf's hedonistic neuron hypothesis.