Selective Maintenance of Value Information Helps Resolve the Exploration/Exploitation Dilemma
Authors: Hallquist Michael N. , Dombrovski Alexandre Y. 
Published: September 2017

Laboratory studies of value-based decision-making often involve choosing among a few discrete actions. Yet in natural environments, we encounter a multitude of options whose values may be unknown or poorly estimated. Given that our cognitive capacity is bounded, in complex environments, it becomes hard to solve the challenge of whether to exploit an action with known value or search for even better alternatives. In reinforcement learning, the intractable exploration/exploitation tradeoff is typically handled by controlling the temperature parameter of the softmax stochastic exploration policy or by encouraging the selection of uncertain options.

We describe how selectively maintaining high-value actions in a manner that reduces their information content helps to resolve the exploration/exploitation dilemma during a reinforcement-based timing task. By definition of the softmax policy, the information content (i.e., Shannon’s entropy) of the value representation controls the shift from exploration to exploitation. When subjective values for different response times are similar, the entropy is high, inducing exploration. Under selective maintenance, entropy declines as the agent preferentially maps the most valuable parts of the environment and forgets the rest, facilitating exploitation. We demonstratein silicothat this memory-constrained algorithm performs as well as cognitively demanding uncertainty-driven exploration, even though the latter yields a more accurate representation of the contingency.

We found that human behavior was best characterized by a selective maintenance model. Information dynamics consistent with selective maintenance were most pronounced in better-performing subjects, in those with higher non-verbal intelligence, and in learnable vs. unlearnable contingencies. Entropy of value traces shaped human exploration behavior (response time swings), whereas uncertainty-driven exploration was not supported by Bayesian model comparison. In summary, when the action space is large, strategic maintenance of value information reduces cognitive load and facilitates the resolution of the exploration/exploitation dilemma.

Author summary

A much-debated question is whether humans explore new options at random or selectively explore unfamiliar options. We show that uncertainty-driven exploration recovers a more accurate picture of simulated environments, but typically does not lead to greater success in foraging. The alternative approach of mapping the most valuable parts of the world accurately while having only approximate knowledge of the rest is just as successful, requires less representational capacity, and provides a better explanation of human behavior. Furthermore, when searching among a multitude of response times, people cannot indefinitely maintain information about every experience. A good strategy for someone with limited memory capacity is to selectively maintain a valuable subset of options and gradually forget the rest. In simulated worlds, a player with this strategy was as successful as a player that represented all previous experiences. When learning a time-varying contingency, humans behaved in a manner consistent with a selective maintenance account. The amount of information retained under this strategy is high early in learning, encouraging exploration, and declines after one has discovered valuable response times.