RLProp

Pick k items so your objectives show up in the ratios you ask for — e.g. 60% relevance, 30% diversity, 10% novelty — not just as tuning knobs that quietly get swallowed by the dominant objective.

RLProp is results-level proportional selection for multi-objective recommendation. You give it target ratios over objectives and a way to score items; it greedily builds a list whose composition matches those ratios, using a mandate-allocation / fuzzy-D'Hondt rule borrowed from how parliaments turn votes into seats. It works for any objectives whose per-item marginal gains you can compute (relevance, diversity, novelty, fairness, calibration, …).

Pure NumPy, one dependency, two functions to learn.

Algorithm: Ladislav Peska & Patrik Dokoupil (SIGIR '22, see Citing). This implementation: Patrik Dokoupil — a standalone, packaged reimplementation, independent of the original experiment code.

Install

pip install rlprop-rs

Quick start

Two ways in, depending on what you already have.

What's a marginal gain? RLProp builds the list incrementally, one item at a time. The marginal gain of item i for objective o is how much adding i to the current (partial) list L improves (or worsens) o — naively o(L ∪ {i}) − o(L). So mgains[o, i] is that quantity for every candidate item and every objective. The naive computation re-evaluates o for each candidate at each step (expensive), but it can often be avoided or sped up dramatically — e.g. additive objectives like relevance have a constant marginal gain, and many objectives admit closed-form incremental updates. See the paper for details and the normalization options that make objectives comparable.

1. You have marginal gains — an (n_objectives, n_items) array. This is the honest core and the fast path:

import numpy as np
from rlprop import RLProp

mgains = np.random.rand(3, 500)            # gains for 3 objectives over 500 items
top_k = RLProp([0.6, 0.3, 0.1]).select(mgains, k=10)   # -> item indices

2. You have objective functions — let rerank build the marginal gains for you (it re-scores at every step, so order-dependent objectives like intra-list diversity work correctly):

from rlprop import rerank
from rlprop import objectives as obj

candidates = np.argsort(-relevance)[:200]  # rerank your model's top-200
recs = rerank(
    candidates,
    objectives=[obj.relevance(relevance), obj.diversity(distance_matrix)],
    weights=[0.7, 0.3],
    k=10,
    normalize="quantile",                  # put objectives on a common scale
)

An objective is just a function f(selected_item_ids) -> float; the three in rlprop.objectives (relevance, diversity, novelty) are conveniences — writing your own is one line.

Two layers, on purpose

The whole public surface is RLProp + rerank. The design is deliberately flat (no plugin zoo) because over-abstraction kills adoption.

	RLProp(weights).select(mgains, k)	rerank(candidates, objectives, weights, k)
You supply	a marginal-gain matrix	objective value functions
Cost	cheap (one pass)	expensive (probes every candidate × objective × step)
Best for	additive objectives, precomputed gains, batch jobs	order-dependent objectives, quick experiments
Normalization	you do it (or normalize_mgains)	built in via normalize=

What you can tune

• weights — target ratios, e.g. [6, 3, 1] (normalized internally).
• allocator — "rlprop" (default), "fuzzy_dhondt" (tie-break toward the larger prospective total), or "weighted_average" (the non-proportional scalarization baseline, for comparison). Or pass your own step function.
• normalize — None, "minmax", "standard", "robust", "quantile" (all pure NumPy; "objectives on the same scale" is what makes ratios meaningful).
• exclude — items to never select (already-seen, blocked, etc.).

How it works

At each step, RLProp looks at how far each objective is from its target share of the gains awarded so far, and picks the item that best fills the largest unfilled mandate — exactly the D'Hondt highest-averages idea, but over continuous marginal gains and with support for negative gains. See the paper for the derivation and the relevance–diversity–novelty experiments.

Relation to the original code & other methods

• The experiments from the SIGIR'22 paper live in the original research repository (moo-as-voting-fast); this package is the streamlined, install-able core extracted from it. The default allocator matches the corrected, fully-vectorized form of that code.

Citing

If you use this software, please cite the paper (GitHub's "Cite this repository" button reads CITATION.cff):

@inproceedings{peska2022rlprop,
  author    = {Peska, Ladislav and Dokoupil, Patrik},
  title     = {Towards Results-level Proportionality for Multi-objective Recommender Systems},
  booktitle = {Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval},
  series    = {SIGIR '22},
  pages     = {1963--1968},
  year      = {2022},
  doi       = {10.1145/3477495.3531787}
}

License

MIT — see LICENSE.