This paper tests how to use neural networks to make long‑run consumption and portfolio choices. The authors study a standard life‑cycle model in which a household chooses consumption and the share invested in a risky asset over a finite horizon that includes working life and retirement. Because the model is low‑dimensional after a common normalization trick, the authors can solve it exactly by dynamic programming and use that solution as a benchmark for neural policies.

They compare four concrete neural architectures. A is a single network conditioned on age. B splits the problem into two networks: one for working life and one for retirement; the retirement network is trained first and then frozen. C trains a separate network for each date by backward induction, where each network is trained against frozen downstream policies. D is C with an added economic shape constraint that forces the marginal propensity to consume (MPC)—the extra consumption from an extra unit of cash—to stay between zero and one. Training uses simulated paths and backpropagates the realized utility through up to 80 time steps. The authors also use practical tricks such as payoff normalization, antithetic sampling, feasibility‑preserving policy maps, and a “direction‑dominant” optimizer that normalizes gradient magnitude.

The study is motivated by the curse of dimensionality: grid‑based dynamic programming becomes infeasible as the number of state variables rises, so researchers often replace the value grid with a neural policy. But in high dimensions there is no ground truth to judge designs. By keeping the state low‑dimensional and using the dynamic‑programming solution as a reference, the authors can isolate the effect of architecture and training choices.

Results show steady gains as the solution is decoupled and trained backward. Moving from A to B to C improves welfare, reduces the Bellman residual (a measure of how well the policy satisfies the dynamic programming equation), and yields more accurate policy functions. The single, time‑conditioned network already performs reasonably but tends to over‑save on average in retirement. The full backward induction (C) reaches within 0.13% of the benchmark in certainty‑equivalent welfare, cuts errors in the consumption share, and greatly reduces the fraction of simulated paths where realized utility falls below the dynamic‑programming reference. However, splitting networks across regimes can create economically implausible behavior: some states imply a negative MPC.