Post 6 of 6. Previous: First-order OCO as a portfolio estimator. Series start: From solving convex programs to tracking them.

This is the merge plan. The mathematics lived in posts 1–5. Here I write down what I would put in a GitHub issue, what I would rebase, what I would delete, and what I would ask a reviewer to run. skfolio 1.0.0 is tagged (2026-08-23). CONTRIBUTING.md asks for an issue before a substantial change, a branch named feature/no-ref/online-portfolio-selection until the issue exists, conventional commits feat(optimization): …, and a PR title prefixed [ENH].¹ The library itself is described in (Nicolini et al., 2025).

The working tree I have is universal_portfolio at about 35 commits ahead of a v0.15.5 merge-base, 0 behind that main, and not rebased onto 1.0. Local HEAD has a dummy message. There is one unpublished commit. None of this is reviewable until it sits on v1.0.0.

Rebase, then cut

Open the issue. Problem statement: skfolio 1.0 can stream moments and re-solve MeanRisk (online_predict); it cannot run Helmbold/Li–Hoi OLPS as BaseOptimization estimators. Link the four-regime glossary (post 1) so “online” is not a fight in the first comment.
Branch from v1.0.0: feature/issue-N/online-portfolio-selection.
Rebase universal_portfolio onto that. Expect collisions in optimization/__init__.py, docs/api.rst, pyproject.toml (autograd), model_selection/ (1.0 already has _online/), and the user guide. 1.0 renamed expend_train → expand_train, FactorModel the estimator → TimeSeriesFactorModel, EWMu.alpha → half_life. The branch will not apply cleanly; that is the work.
Delete from the rebased tree everything in the out-list below before opening the PR. A 19k-line dump with SWORD and Cover leftovers is not a research PR. It is a hostage situation.

Commit hygiene after the rebase: one commit for the engine and estimators, one for tests, one for docs/gallery, or a single well-messaged feat(optimization): add online portfolio selection estimators if the history is otherwise noise. Do not ship the 35-commit diary (... messages included). Squash onto 1.0, then optionally split the squash by area so a reviewer can read git log origin/main..HEAD --stat.

skfolio.optimization on 1.0 must still look like 1.0 plus a new subpackage. MeanRisk, _fit, compact accelerate, and online_learning.rst stay untouched.

Issue body (paste-ready outline)

Problem. Cannot run EG/OLMAR as sklearn estimators; 1.0 online_* is streaming MeanRisk.
Glossary. Four regimes (link post 1). partial_fit on MeanRisk vs on FollowTheWinner.
Scope. In-list / out-list below.
Integration invariant. After partial_fit, weights_ is the next traded book; predict(X_test) applies that book to a future window; fit_predict is the sequential in-sample path.
Non-goals. No MeanRisk _fit change, no accelerate import, no C solver, no autograd core dep.
Docs. Gallery under examples/online_learning/, new olps.rst, see-also on online_learning.rst.

In the first PR

Package. src/skfolio/optimization/online/ with public:

FollowTheWinner — strategy="eg" and "ogd", learning_rate="auto", default log-wealth, update_mode FTRL or OMD if both are tested equal on EG.
FollowTheLoser — olmar, pamr, rmr, cwmr, update_mode="pa" only.
CRP, UCRP, BestStock, BCRP (MeanRisk, LOG_WEALTH default).
regret(..., regret_type=STATIC) and RegretType.STATIC.

API verbs. fit (row loop), partial_fit (one row), fit_predict → MultiPeriodPortfolio, predict_online for continuation. Inherited predict remains, documented as lookahead if you pass the training stream.

Constraints. Box plus budget, optional L1 max_turnover against last trade. Transaction costs and management fees against drifted holdings, first period free unless previous_weights is passed. clone / get_params / set_params must work; learned state in weights_, all_weights_, wealth_, all_wealth_.

Docs. A gallery example under examples/online_learning/ (the 1.0 folder), e.g. EG vs UCRP vs BCRP on load_sp500_dataset after prices_to_returns, evaluated with fit_predict. A user-guide page that links online_learning.rst and spends the first screen on the glossary: streaming MeanRisk vs OLPS. docs/api.rst autosummary. optimization/__init__.py re-exports the public names.

Dependency. Analytic log-wealth gradient. No autograd in pyproject.toml core deps. The PR template asks.

Tests (minimum I would not merge without):

clone / get_params / set_params round-trip.
partial_fit rejects two rows.
EG multiplicative identity on a tiny simplex (match w \odot \exp(-\eta g) then normalize).
OGD equals projected gradient for Euclidean \(\psi\).
fit is sequential: permuting rows changes all_weights_ (time-series, never shuffle).
fit_predict wealth path vs a manual loop of partial_fit.
UCRP is \(1/n\) every period.
Static regret vs BCRP is nonnegative on log-wealth up to a stated atol.
Costs: drifted-holdings example from the user guide, first period zero cost without previous_weights.
online_predict smoke: warmup, test_size=1, returns MultiPeriodPortfolio, no pipeline.
predict(X_train) after fit(X_train) is not equal to fit_predict (lookahead trap as a documented test, not a failure).

Li–Hoi relatives loaders (load_nyse_o_relatives_dataset, …) can ship if they are small and already in datasets/. If they bloat the wheel, keep them out of the first PR and use load_sp500_dataset.

Out of the first PR

SWORD family, Ada-BARRONS, TsallisMirrorMap, deprecated log-barrier.
FollowTheLoser(update_mode="md"), CWMR mirror-descent.
objective= CVaR/EVaR/CDaR on a single period (path measures at \(T=1\) are proxies; autograd factory).
RegretType.DYNAMIC_UNIVERSAL, DYNAMIC_WORST_CASE as public API (keep STATIC; prefix-BCRP dynamic can wait).
Cover Universal Portfolios, CORN/BNN, Anticor, named ONS.
Public FirstOrderOCO, public online_walk_forward_predict.
autograd required.
Any change to MeanRisk._fit, any import of skfolio_accelerate, any C sequential solver, any ADMM continuation kernel.
Replacing 1.0 online_predict semantics.

prod / Burg: second PR unless the rebase makes it free (tests already green, no extra docs). I would still hide it behind the internal engine.

Naming

Name in 1.0	Meaning	Name to add
`online_predict`	one clone, `partial_fit` stream, path score	keep
`docs/user_guide/online_learning.rst`	EW moments + repeated convex solves	keep, add a “see also OLPS” paragraph
`skfolio.optimization.online`	OLPS estimators	add
`docs/user_guide/olps.rst` (preferred name)	Helmbold / Li–Hoi	add; do not overwrite `online_learning.rst`

If the branch’s online.rst is copied onto online_learning.rst, the PR should be closed.

Reviewer script

From a clean 1.0 venv, after uv pip install -e ".[dev]":

uv run pytest tests/test_optimization/test_online -q
uv run pytest tests/test_model_selection/test_online -q
uv run ruff check src/skfolio/optimization/online tests/test_optimization/test_online

Then the gallery script, manually:

from sklearn.base import clone
from skfolio.datasets import load_sp500_dataset
from skfolio.model_selection import online_predict
from skfolio.optimization.online import FollowTheWinner, UCRP, BCRP, regret
from skfolio.preprocessing import prices_to_returns

X = prices_to_returns(load_sp500_dataset())
eg = FollowTheWinner(strategy="eg")
path = eg.fit_predict(X)
assert path.returns.shape[0] == len(X)

frozen = clone(eg).fit(X).predict(X)  # lookahead on purpose
# frozen.returns is w_T applied to every row; path is not that

ucrp = UCRP().fit_predict(X)
R = regret(FollowTheWinner(strategy="eg").fit(X), X)
assert R[-1] >= -1e-6

online_predict(FollowTheWinner(strategy="eg"), X, warmup_size=60, test_size=1) should return a MultiPeriodPortfolio whose first test date is after warmup. If it applies predict internally instead of predict_online / per-row weights, that is a bug in the integration, and it is on us to patch the OLPS estimator’s predict or to teach online_predict a method= for online estimators. I would prefer the estimator grow a flag or predict that uses last-period weights for a future test window (causal) while fit_predict remains the in-sample sequential path. That design choice has to be explicit in the issue, because 1.0 online_predict currently assumes predict(X_test) after partial_fit is the right out-of-sample map, which is true for MeanRisk (frozen book on the next window) and true for EG only if weights_ is the book you trade next, applied to the test window without refitting inside predict. That last sentence is the integration invariant. Write it on the issue.²

Follow-up issues (named, not in the diff)

A. Richer projections. Groups, linear inequalities, tracking-error, variance bound via the existing cvxpy project_convex. Tests against MeanRisk-feasible random points.

B. Clarabel in-place updates. Accelerate’s scenario path is 2–4× because cones rebuild. Upstream or in accelerate, not in optimization/online.

C. Solver-state continuation as a benchmark. Persistent OSQP \(x,y\) (already there) plus factorization reuse on expanding \(T\), measured on the 20-year table. Accelerate issue. Success criterion: iteration counts, not a new public class.

D. SequentialSolver C library. Only after B and C have numbers. Canonical QP/cones in, state out. No MeanRisk in the ABI. Separate repository.

E. prod, AdaGrad, then SWORD. One strategy family per PR once A is stable.

F. Pattern matching / Cover UP. Only with a dataset and a test that is not “it runs.”

What success looks like

A maintainer who knows MeanRisk and has not read Hazan can clone the branch, run the gallery, see EG next to UCRP, read that predict lookaheads, and leave src/skfolio/optimization/convex/ grepless in the diff. The issue uses the word “online” with a glossary. Accelerate is cited as evidence that WalkForward is a trajectory, then left alone. The C solver is a footnote.

That is a research-level PR onto 1.0.0. It is also smaller than the branch I already wrote. The cut is the contribution.

PR title tags in the template are [ENH], [MNT], [DOC], [BUG]. New estimators also need the gallery and docs/api.rst or the docs CI fails.⏎
MeanRisk after partial_fit: weights_ is the solution of \(P(\theta_t)\), and predict(X_test) applies that frozen book to the next window. EG after partial_fit: weights_ is \(w_{t+1}\), the book for the next unobserved relative. Both are valid predict semantics. Mixing them in one paragraph without the glossary is how the review stalls.⏎

References

Nicolini, C., Manzi, M., & Delatte, H. (2025). skfolio: Portfolio Optimization in Python. Proceedings of the International Research and Industry Symposium on AI (IRIS-AI 25), 35–41. https://doi.org/10.65236/iris-ai/proceedings/2025/article/3