Schedule of Events | Symposia

Defining the optimal form for subjective value encoding by the brain, a numerical approach

Poster Session B - Sunday, March 30, 2025, 8:00 – 10:00 am EDT, Back Bay Ballroom/Republic Ballroom

Shreya Sinha¹ (ss14468@nyu.edu), Agnieszka Tymula², Paul Glimcher¹; ¹Grossman School of Medicine, New York University, ²School of Economics, University of Sydney

While early studies hypothesized that internal value representations should be linear or logarithmic transformations of objective value, empirical evidence from recordings in monkeys show sigmoidal functions. Building on efficient coding theory, our groups have proposed a divisive normalization-style representation, which is optimal for Pareto III environments. Rather than relying on empirical observations to infer efficiency, here we invert this approach by explicitly defining the nervous system’s objective as maximizing long-run reward rates. We then use a mixture of analytical and numerical methods to answer: What specific encoding function is reward maximizing? (Parallel investigation explores error-minimizing functions.) Our findings reveal that for a near-perfect encoder (as noise goes to zero in the limit) a linear encoding function is always optimal, but as encoding noise increases, sigmoidal and curved functions emerge as reward-maximizing. Additionally, as the number of drawn options increases, the optimal functions exhibit a rightward shift. An optimal encoder at any given (non-zero) noise level changes with the distribution of rewards in the environment and the number of options drawn from that environment that the nervous system faces. These results suggest that the sigmoidal value functions, like those of Kahneman and Tversky, are optimal for mid-noise systems facing uniformly distributed rewards, while logarithmic encoding suits exponentially distributed environments like the one studied by Bernoulli. Our research unveils a striking resemblance between derived and biological utility functions in the brain, hinting at optimality under specific constraints. It also offers deeper insights into the mechanisms underlying human choice behavior.

Topic Area: THINKING: Decision making