Nonlinear modulation of human exploration by distinct sources of uncertainty

Decision-making in uncertain environments requires balancing exploration and exploitation, with exploration typically assumed to increase monotonically with uncertainty. Challenging this prevailing assumption, we demonstrate a more complex relationship by decomposing environmental uncertainty into volatility (systematic change in reward contingencies, learnable) and stochasticity (random noise in observations, unlearnable). Across two behavioral experiments (N=1001, N=747) using a probabilistic reward task, we find a robust U-shaped relationship between the volatility-to-stochasticity (v/s) ratio and exploratory behavior, with participants exploring more when either stochasticity or volatility dominates. Remarkably, this pattern extends to real-world financial behavior, as demonstrated through analysis of five years of S&P 500 stock market data, where portfolio diversity (a proxy for exploration) shows the same U-shaped relationship with market volatility (systematic price movements driven by fundamental factors, e.g., economic shifts) relative to trading noise (random fluctuations from trading activity unrelated to fundamentals). These findings reveal how humans adaptively modulate exploration strategies based on the qualitative composition of uncertainty, with optimal performance occurring at intermediate uncertainty ratios. This nonlinear relationship has important implications for understanding decision-making across domains where uncertainty arises from multiple sources.