Deep Learning for Dynamic Programming with Recursive Utility Using First-order Conditions
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摘要
CEFOL introduces a Certainty-Equivalent First-Order Learning algorithm that solves discrete-time dynamic programming with recursive utility by learning the state-control certainty-equivalent C(s,t). It decouples the nonlinear certainty-equivalent transformation from policy updates by using a dedicated neural network for C(s,t). The method trains value, policy, multiplier, and C networks via model-specific first-order residuals (Euler/KKT), enabling direct handling of equality and inequality constraints without penalty terms. The approach applies to risk-sensitive, Epstein–Zin, small-noise robust-control, and DSGE models, achieving small out-of-sample Bellman errors and residuals (order 10^-4 to 10^-3) and close alignment with VFI benchmarks when available. It also generalizes to expected utility as a special case and supports vector controls and occasionally binding constraints; this framework provides diagnostics (Bellman errors and residuals) for value consistency and policy optimality [page::1][page::2][page::3][page::4].
