Research Reports

Research Reports

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PhD research at Hiroshima University, in the Urban and Transportation Planning Laboratory under Prof. Makoto Chikaraishi.

The work is about constraint heterogeneity in dynamic choice models. The object is a Markov perturbed-utility model with heterogeneous feasible sets: one shared state graph, a family of feasible sets over it, and the question of how many distinct computations that family actually requires.

Status

The framing below is current as of October 2026 and is being taken to a supervisor session, not settled by it. The research directions at the end are themes to read into — they carry no ordering and no commitment. Where this page and the working documents disagree, the working documents win.

A day is assembled out of what is possible

Not only out of what is wanted. Hägerstrand’s capability, coupling and authority constraints classify why a person cannot do something, treating constraints as the subject rather than as a modelling nuisance.

And what is possible differs between people. Kwan (2000) finds gender differences in the fixity of constraints — the empirical reason to treat constraints as individual rather than uniform. Sen’s conversion factors make the general point: the same resource yields different achievable functionings for different people, depending on the person, the society and the built environment. Transposed here, the same city yields different achievable days. Same network, same opening hours, different free time, because what you can convert the city into depends on where you live, who you collect, and when you are due somewhere.

In the survey the diaries used here come from, 6,231 of 10,634 individuals have a recorded workplace and 2,994 of 5,288 households have more than one member. Those are survey-wide counts, not shares of the estimation sample.

Why that matters for the model

There is a published path from the time-geographic prism to a money-valued accessibility measure: Karlström (2005) put the prism inside a dynamic programme, Jonsson et al. (2014) named the bridge in their own title, Västberg et al. (2020) estimated the full model with constraints exact and per person, and Naqavi et al. (2023) define spare-time accessibility directly as the value function and report it in money.

So the value at the start of the day is the set of achievable days, priced. Mis-specify the constraints and the number being reported is wrong, not merely imprecise.

The problem, in one sentence

A model that cannot carry per-person constraints reads constraint as preference. A parent who never shops in the evening because of a pickup looks like someone who dislikes evening shopping, and the error propagates into accessibility, welfare, and who is said to gain from a policy.

Models that can carry it exactly pay one value function per person — which is why that lineage turned to sampling alternatives, and gave up the full-support sum a welfare reading needs.

Constraint heterogeneity is therefore either misattributed or unaffordable. The work is about removing the second horn.

Where the work sits

Perturbed utility splits a choice model in two: the domain, which is what is available at all, and the objective, which is how probability spreads over what is available. Written over flows, the penalty has one term for each.

Every neighbour in this literature works the objective — sparse perturbations, generalised entropies, Fenchel-Young losses. Their domain is flow conservation: network structure, identical for every traveller. The slot exists in their own formulation and carries nothing personal.

This work varies the domain instead: one feasible set per person, built from attributes that are not in the graph at all.

Representing that affordably needs three things at once — a shared structure many people are solved against, a mask on it that depends on who is being solved, and many such masks indexed by person. Pointing at where each is, or is missing, in a neighbour’s own notation is what makes this a position rather than a complaint:

shared structuremaskmany masks
Västberg et al. (2020)—n/a✓
Naqavi et al. (2023)—n/a✓
Oyama & Hato (2019)✓✓—
Fosgerau & Yao (2026)✓—n/a

Västberg has the person index without a shared structure, so heterogeneity is handled by replication and cost is linear in people. Oyama has the shared structure and the mask — on a layered acyclic graph, with a reachability cone, introduced for exactly this reason — but the context is a single origin–destination pair, and his own footnote calls the per-pair version “a trade-off between computational efficiency and realism” and declines it. Fosgerau and Yao have the sharing, and their feasible set carries no person at all; their heterogeneity is in volume, not in feasibility.

Each has two of the three. Nobody has asked how many distinct masks a real population needs.

Two concessions belong with that table. Västberg’s constraints are exact, not soft — the shortfall is cost, not correctness. And sampling of alternatives is consistent — the shortfall is efficiency plus the full-support sum, not validity.

The organising question

What decides the cost is not which Hägerstrand type a constraint is, but what it reads — and the decisive question is whether the thing it reads is itself a choice.

Write each constraint as a rule reading some attributes and a state. Then it either reads nothing about the person, so it is removed once for everybody; or reads an attribute with few values, so it selects one of a handful of prebuilt structures; or reads something nearly unique to the person, so it is switched off against a structure everyone shares; or it reads another person’s day, in which case it is not a rule about this person at all.

That last case is the boundary, and it is a principled one rather than a practical one. The work handles every constraint whose referent is given — including coupling in Hägerstrand’s sense, because an employer’s schedule is given. What it cannot handle is coupling whose counterpart is also optimising.

What that costs, measured

7,468 real diaries need four structures. A synthetic population of 214,216 people for the same city needs the same four. Separately, 8,031 people need 3,096 solves rather than 8,031 — a 2.6× collapse. Per-person switching leaves 93.3–96.2% of states and 80.4–87.8% of edges live, so roughly a sixth of edge work is swept and discarded in exchange for one batched solve instead of hundreds of builds.

The reason the per-person case is affordable at all is the clock: every action advances it, so the graph is acyclic and a solve is one backward sweep rather than a linear system. That is a property of modelling a day, not an achievement. What it buys is room — because solving is cheap, the question can move from how do we solve this at all to how do we embed constraints that differ person to person.

What is deliberately not claimed

Stated here because all of it has drifted into earlier drafts:

  • Not that constraints exist in these models, or that they are per person
  • Not that zero-probability enforcement is new
  • Not that the layered acyclic graph, the reachability cone or an edge mask inside the sum is new — those are Oyama and Hato’s, introduced for the same reason
  • Not that the perturbed-utility formulation is ours; with entropy this is recursive logit, which is 2013
  • Not that the value function as an accessibility measure is new — that is the published bridge above
  • Not that schedulers cannot be estimated, and not that sampling is invalid
  • Not that the cost result transfers to cyclic models. That is open, not claimed

The honest limits are stated too: value of time comes out at 193 yen per minute against the reference model’s own 44, because fuel-only car cost is proportional to distance and the cost and time coefficients are collinear; one finite penalty survives in the specification, on the lower bound of work start; household coupling does not factorise; the modelled horizon is chosen rather than given; and three of the five constraint sources need an exogeneity argument that has not yet been made.

Where this goes

The classification cuts across Hägerstrand’s three types, and two dropped assumptions give the thesis its shape:

acyclic, a daycyclic, a network
reads given quantitiesthe first paperdoes masking admit a low-rank resolvent update?
reads another’s choiceendogenous coupling, estimable and welfare-bearingboth at once

The first paper is one cell. The rest is the same question with the acyclicity and the given-referent assumptions dropped, rather than a new topic. Six directions are currently written as themes to read into, not as papers: what per-person feasibility costs when the clock condition fails; which shared representation is best, and whether there is a principled way to choose one; constraints between people, and where exactly the boundary is; constraints that change under a policy scenario; constraints that are uncertain, which is flagged as outside the current frame because it breaks the known-arrival assumption; and where constraints come from, when feasibility must be inferred rather than read off.

Each carries an honest risk line — whether the machinery is so established that the contribution would be the application rather than the method. The reading is what settles that, and it has not happened yet.

Where this comes from: the Master’s framework

The computational ground this stands on was the Master’s thesis, A Scalable Computational Framework for Activity-Based Dynamic Discrete Choice Models (Hiroshima University, September 2026; defended 27 July 2026).

Its problem was that the value function has to be re-solved at every trial parameter vector, over a state space that is a product of zones, activities, modes, clock and duration. Stored densely the transition structure runs to the order of 10¹² entries, and a naive solve runs to tens of hours. Västberg et al. put exact nested-fixed-point estimation of their own case study at roughly a thousand CPU-days and sampled instead.

The observation it turned on is the one the current work inherits: a log-sum adds up every feasible day and is strictly increasing in every term, so nothing may be discarded for being unlikely — only for being impossible. Three contributions followed. A forward search under the space-time prism keeps only the states a person can physically reach, cutting the theoretical state space by more than ninety-nine percent, exactly rather than approximately. The pruned graph is acyclic, so a whole time layer solves in one scatter-reduce call instead of state by state. And because feasibility is shared where preference is not, one graph serves everyone facing the same constraints.

On Higashihiroshima — 144 zones, 7,376 valid persons, four topology groups serving 259 evaluation contexts — building the shared graphs took about 125 s once, and masking and solving one evaluation context took 1.56 s on average, about 1,844 people per build.

What the thesis left open is where the PhD starts: standard errors, welfare confidence intervals, and faster estimation. The current frame is a different question from that list, though — not how to compute the model faster, but what per-person constraints cost, and what that implies about which differences between people need their own computation.

Decks

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