Meeting Document

Item Content
Name Azwan Nazamuddin
Meeting Date 2026/05/11
Previous Meeting Date 2026/04/27

1. What I Want to Discuss Today (Most Important)

  1. K=10 estimation results and the work-start timing gap. The full NFXP estimation has converged with all 10 parameters statistically significant (LL = −19,187). However, behavioral validation reveals that the model predicts agents begin work at approximately 14:51, whereas the observed average is approximately 8:30. I want to discuss whether this gap indicates a utility function misspecification that must be resolved before Phase B (welfare infrastructure), and what approach to take.

  2. JSPS proposal writing. The 6-move hourglass narrative structure and citation list are in place, but the proposal is not yet finalized — the prose is still too dense and needs to be made more compact to leave room for illustrations. I want feedback on which parts to condense and where illustrations would be most effective.

2. Current Situation (Progress Since Last Meeting)

What I did

Gradient debugging and bug fixes. I identified and corrected two bugs in the NFXP analytical gradient computation. The first was the omission of forbidden-mask constraints from the gradient backward induction: states that are structurally impossible for a given agent (e.g., a home zone that is not theirs) were accumulating spurious gradient values. The second was a zone-ID indexing mismatch — the gradient code used 1-indexed activity-enum values to key the forbidden-mask dictionary, while the state tensor stores zone IDs as 0-indexed integers, causing the wrong home zone to be masked for every agent. Both bugs corrupted all gradient computations in every previous run. I validated the corrected gradient on 7 synthetic micro-graph test cases (7/7 pass).

A3 diagnostic estimation. With c_change fixed at −0.3 (the Hiroshima Household MNL prior), I estimated the remaining 9 parameters freely using BFGS with the corrected gradient. All 9 parameters converged to economically valid signs within 4 iterations (best LL = −35,584; delta = 0.041, mu_home = 0.062). This confirmed that the analytical gradient is working correctly.

K=10 unconstrained estimation (BFGS). Releasing c_change as a free parameter, I ran K=10 BFGS warm-started from the A3 best checkpoint. The key positive result: c_change found an interior MLE at −0.366, rather than drifting to −∞ as in all pre-fix runs. This confirms that the c_change identification failure was caused by the gradient bugs. The negative result: delta and mu_home both became negative at the best point (LL = −31,264), indicating the unconstrained optimizer entered an economically invalid region.

K=10 L-BFGS-B estimation (final, bounded). Switching to L-BFGS-B with lower bounds (delta ≥ 0, alpha ≥ 0, beta ≥ 0, mu_home ≥ 0; c_change ∈ [−5, 0.5]) and warm-starting from the A3 checkpoint, the optimizer converged in 18 iterations (LL = −19,187.07, 825 valid persons, 48,908 observed steps). BHHH standard errors were then computed from the analytical gradient scores. All 10 parameters are statistically significant (see Section 7).

Work timing analysis. I produced an interactive HTML report analyzing why the model predicts a substantially later work-start time than observed. The report includes per-parameter utility plots and simulation validation and is available at: work_timing_analysis.html

Literature reviews. I completed 11 new literature reviews, covering papers for JSPS proposal Moves 1–3 and background for Phase B. These are listed in Section 8.

JSPS proposal outline. The 6-move hourglass narrative structure and citation list are complete. All papers cited in Moves 1–5 are in the vault with full literature review notes. The proposal itself, however, is not yet finalized — the current draft is too text-heavy and needs revision to make it more compact and to free up space for illustrations. The LaTeX source is on Overleaf: JSPS DC Proposal (read-only)

Thesis writing approach. The 3 - Permanent Notes/reports/thesis folder is now for research plans, writing notes, and TODOs only. Actual thesis writing has moved to Overleaf: Thesis (read-only)

What I could not do / What is delayed

Full numerical Hessian. Three attempts to compute the full numerical Hessian were killed by GPU out-of-memory errors from an external process on the shared machine. Only BHHH standard errors are available. The full Hessian (~9 hours, 66 evaluations) has not been reattempted.

Behavioral validation. The work timing analysis reveals a substantial discrepancy: the model predicts agents begin work at ~14:51, while the observed average is ~8:30. The source of this discrepancy — whether it is utility function misspecification, a data coverage issue, or an interaction between schedule-constraint parameters — has not yet been identified.

Phase B (welfare infrastructure). Phase B has not been started. It was held pending confirmation that the K=10 results are behaviorally valid. Whether to proceed to Phase B now or first resolve the timing gap is the central question for today’s meeting.

3. Definitions of Terms

Term Definition
NFXP Nested Fixed-Point estimation: the full backward induction over the state space is solved exactly at every likelihood evaluation during optimization. No approximation of the value function.
L-BFGS-B A bounded variant of the limited-memory BFGS quasi-Newton optimizer. “Bounded” means it enforces box constraints on parameters, used here to impose economic sign restrictions (e.g., delta ≥ 0).
BHHH Berndt-Hall-Hall-Hausman standard error estimator. Approximates the Fisher information matrix as the outer product of individual score vectors. Used here as a substitute for the full numerical Hessian when GPU memory prevents the latter.
Forbidden masks In backward induction: constraints that prevent agents from occupying structurally impossible home-zone states. Without these, invalid states accumulate spurious value-function contributions that corrupt the gradient.
Schedule delay cost The disutility incurred when an agent arrives at work earlier (penalized at rate α per min²) or later (penalized at rate β per min²) than their scheduled start/end time.
Phase B The welfare infrastructure phase: deriving and implementing the log-sum compensating variation measure from the DDCM value function (McFadden 1981; Small & Rosen 1981).

4. My Own Thoughts

On discussion item 1 — K=10 results and the work-start timing gap

Current thought: The work-start timing gap is a structural misspecification of the utility function. The estimated pre-schedule earliness penalty (α = 0.0011/min²) implies that working is worthwhile starting δ/α = 37 minutes before the scheduled start. However, the home reservation utility (μ_home = 0.062/min) is large relative to the net expected utility of departing for work in the early morning — accounting for travel cost and the pre-schedule penalty while the schedule has not yet started. The model therefore finds it rational for agents to stay home until much later in the day, when the on-schedule reward δ dominates.

Reasoning: This is structurally analogous to the c_change identification problem from earlier in estimation. Just as constant-marginal-utility SHOP/LEIS had no satiation mechanism to stop over-chaining, the current morning utility structure has no mechanism to make early departure attractive. A time-of-day preference component, or a richer representation of the morning congestion window, could address this.

Alternatives I considered: Both directions below are tentative and need more discussion before any commitment is made. (a) Make the HOME utility non-flat: currently μ_home is constant per minute throughout the day, but if it decreases over the morning it would naturally push agents out of home earlier. (b) Make the WORK on-schedule utility non-flat: a time-varying δ(t) that is higher closer to t_s and declines away from it could more strongly attract agents toward the observed departure window than the current flat δ. I am not confident about either and want to discuss further before going in any direction.

On discussion item 2 — JSPS proposal

Current thought: The 6-move hourglass argument is coherent and the citations are confirmed. The problem is density: the current draft fills every available line with text, leaving no room for illustrations. An illustration of the hourglass structure itself, or a diagram showing the two bridges (Bridge 1: MaxEnt IRL ≡ logit DDCM; Bridge 2: BI ≡ semiring message-passing), would communicate the core idea faster than prose — but only if text is cut to make space for them.

Reasoning: The JSPS committee evaluates (a) societal and academic significance, (b) originality, and (c) feasibility. Moves 1–2 address (a); Move 5 (welfare preservation criterion, Structural-IRL) addresses (b); the master thesis result (>99% state pruning, exact GPU BI) addresses (c). Illustrations placed at Moves 4–5 would sharpen (b) and (c) significantly, but they require compressing the background moves — especially Move 2’s three-point list and the bridge connector paragraph.

Alternatives I considered: (a) Cut Move 1 to two sentences and use the space for a bridge diagram at Move 5. (b) Replace Move 2’s three-point list with a single sentence plus a small timing-cost figure. (c) Keep the current text-heavy draft and drop illustrations entirely — but this risks the proposal reading as dense and hard to follow at a glance.

5. Where I Am Stuck / What I Cannot Decide on My Own

  • Timing gap vs. Phase B priority. I cannot determine on my own what degree of behavioral fit is required before the welfare measure is reliable. If the model mispredicts work-start timing by ~6 hours, any Phase B welfare estimate for a peak-hour congestion policy could be systematically wrong. Fixing the utility structure means another full estimation cycle — potentially weeks. I need the supervisor’s judgment on whether Phase B can proceed with the current model (with the limitation documented), or whether the utility structure must be corrected first.

  • JSPS compaction and illustrations. I cannot determine on my own which paragraphs can be cut without weakening the argument, nor where illustrations would be most persuasive given the page limit. The current draft is too dense to accommodate figures. I need the supervisor’s view on which moves to shorten and whether a bridge diagram or a timing figure would be worth the space cost.

6. Things I Want to Confirm

  • Is the BHHH standard error acceptable as the primary SE report for the hEART short paper, given that the full numerical Hessian was not computed?
  • What is the submission deadline for the JSPS DC proposal, and should it be written in English or Japanese?

7. Computational Results / Figures

Result Link Notes
Work timing analysis work_timing_analysis.html Model predicts work start ~14:51; observed ~8:30. Interactive utility plots. Code: private ddcm repo.
K=10 parameter estimates + BHHH SEs Table below LL = −19,187.07; 825 valid persons; 48,908 steps; 28 graph groups

K=10 Converged Parameters — L-BFGS-B, Analytical Gradient:

Parameter Description Estimate SE (BHHH) t-stat
δ WORK on-schedule marginal utility (per min) 0.04078 0.00030 136.5 ***
α Pre-schedule earliness penalty 0.00110 0.00036 3.1 **
β Post-schedule lateness penalty 0.00301 0.00004 68.6 ***
β₁_shop SHOP attractiveness × P_open coefficient 0.32328 0.01158 27.9 ***
β₀_shop SHOP base marginal utility (per min) −0.79548 0.00271 −293.3 ***
β₁_leis LEIS attractiveness × P_open coefficient 0.39185 0.00104 377.4 ***
β₀_leis LEIS base marginal utility (per min) −0.26516 0.00098 −271.4 ***
c_change Switching cost (per departure + arrival) −0.30132 0.02842 −10.6 ***
μ_home HOME reservation threshold (per min) 0.06175 0.00018 342.8 ***
θ_travel Travel time cost scaling 1.03633 0.01665 62.2 ***

***: |t| > 2.576 (1%), **: |t| > 1.960 (5%)

8. Supplementary Materials

New literature reviews this week:

Paper Topic Used for
Eliasson et al. (2009) Stockholm congestion trial: 22% traffic reduction, public opinion reversal after living experience JSPS Move 1 — societal motivation
Small (1982) Empirical schedule delay costs: w_p ≈ 0.5×wage, w_j ≈ 1.5×wage JSPS Move 2 — why timing matters
McFadden (1981) Log-sum welfare measure — Williams-Daly-Zachary theorem JSPS Move 3 + Phase B welfare foundation
Small & Rosen (1981) Compensating variation for discrete choice goods JSPS Move 3 + Phase B welfare foundation
Keane & Wolpin (1994) Value-function interpolation (simulation + interpolation) Background — positioning against approximate methods
Rust (1997) Randomization to break the curse of dimensionality Background — DDCM computational complexity framing
Kalouptsidi (2021) Identification of counterfactuals in DDCM Phase B — partial identification of welfare measures
Bajari, Benkard & Levin (2007) Two-step estimation for dynamic games Background — two-step vs. NFXP strategies
Tsitsiklis & Van Roy (1997) TD learning convergence with function approximation Phase C background — Bridge 1 theoretical foundation
Van Hulsel et al. (2009) RL-based activity-travel simulation (pre-MaxEnt IRL era) Phase C background — Bridge 1 historical context
Fosgerau et al. (2024) Estimating PUM route choice with individual-level data Phase B/C background — individual-level estimation

Links:

Action Items for Next Meeting (fill in after the meeting)

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