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arxiv: 1907.04484 · v1 · pith:47KLRIIMnew · submitted 2019-07-03 · 💻 cs.LG · cs.AI· stat.ML

Co-training for Policy Learning

Jialin Song , Ravi Lanka , Yisong Yue , Masahiro Ono This is my paper

Pith reviewed 2026-05-25 10:16 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords co-trainingpolicy learningreinforcement learningimitation learningsequential decision makingmultiple representationscombinatorial optimization
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The pith

Sufficient conditions allow co-training from two state-action views to improve policies over single-view learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies sequential decision-making policies when multiple state-action representations exist, as occurs in planning with different integer programming formulations or combinatorial problems with both integer and graph views. It adapts the classical co-training idea from classification to derive sufficient conditions where two views produce better policies than either alone. A meta-algorithm is introduced that works with reinforcement learning and imitation learning, and experiments demonstrate gains on discrete and continuous control tasks plus combinatorial optimization problems.

Core claim

Under sufficient conditions, learning from two complementary state-action representations improves upon learning from a single representation alone, and this improvement is realized by a meta-algorithm for co-training that is compatible with both reinforcement learning and imitation learning.

What carries the argument

The co-training meta-algorithm that alternates training between two views to mutually refine the policy.

If this is right

  • Policy quality improves when multiple formulations of the same decision problem are available and used together.
  • The meta-algorithm applies equally to reinforcement learning and imitation learning settings.
  • Gains are observed on both discrete/continuous control and combinatorial optimization tasks.
  • The approach directly extends co-training concepts from classification into sequential decision making.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Identifying pairs of complementary representations may be a practical bottleneck even when the theoretical conditions hold.
  • The framework could be extended to more than two views if the mutual-improvement conditions generalize.
  • Sample efficiency in reinforcement learning might increase when dual representations reduce the need for exploration in each view separately.

Load-bearing premise

The two representations supply complementary information that permits each view to improve the policy quality obtained from the other.

What would settle it

A controlled experiment in which two views satisfy the stated conditions yet produce no measurable improvement in policy quality over the single-view baseline.

Figures

Figures reproduced from arXiv: 1907.04484 by Jialin Song, Masahiro Ono, Ravi Lanka, Yisong Yue.

Figure 1
Figure 1. Figure 1: Two ways to encode minimum vertex cover (MVC) problems. Left: policies learn to operate directly on the graph view to find the minimal cover set [30]. Right: we express MVC as an integer linear program, then polices learn to traverse the resulting combinatorial search space, i.e., learn to branch-and-bound [23, 56]. (i.e., regret) versus the optimal policy. These theo￾retical characterizations shed light o… view at source ↗
Figure 3
Figure 3. Figure 3: Graphical model encodes the conditional inde [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Discrete & continuous control tasks. Experiment results are across 5 random seeded runs. Shaded area [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of CoPiEr with other learning￾based baselines and a commercial solver, Gurobi. The y-axis measure relative gaps of various methods com￾pared with CoPiEr Final. CoPiEr Final outperforms all the baselines. Notably, the gaps are significant because getting optimizing over large graphs is very challenging. selection policy for branch-and-bound search. A node selection policy determines which node to… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of CoPiEr with other learning￾based baselines and a commercial solver, Gurobi. The y￾axis measure relative gaps of various methods compared with CoPiEr Final. CoPiEr Final outperforms all the baselines. Notably, the scale of problems as measured by the number of integer variables far exceed previous state-of-the-art method [56]. aggregating both policies. The effectiveness of CoPiEr enables solv… view at source ↗
Figure 7
Figure 7. Figure 7: Two views for Risk-Aware Path Planning. On [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

We study the problem of learning sequential decision-making policies in settings with multiple state-action representations. Such settings naturally arise in many domains, such as planning (e.g., multiple integer programming formulations) and various combinatorial optimization problems (e.g., those with both integer programming and graph-based formulations). Inspired by the classical co-training framework for classification, we study the problem of co-training for policy learning. We present sufficient conditions under which learning from two views can improve upon learning from a single view alone. Motivated by these theoretical insights, we present a meta-algorithm for co-training for sequential decision making. Our framework is compatible with both reinforcement learning and imitation learning. We validate the effectiveness of our approach across a wide range of tasks, including discrete/continuous control and combinatorial optimization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper studies co-training for sequential decision-making policies when multiple state-action representations are available. It states sufficient conditions under which two views yield mutual policy improvement over a single view, introduces a meta-algorithm compatible with both reinforcement learning and imitation learning, and reports empirical results on discrete/continuous control and combinatorial optimization tasks.

Significance. If the sufficient conditions are shown to hold in the evaluated domains and the reported gains are attributable to the co-training mechanism rather than other factors, the work would supply a principled extension of classical co-training to policy learning and a practical meta-algorithm for domains that admit multiple formulations.

major comments (2)
  1. [§3 and experimental sections] §3 (sufficient conditions): the manuscript states conditions under which two views permit mutual improvement, yet the experimental sections provide no verification that any evaluated task satisfies these conditions (e.g., no reported measurement of view disagreement, conditional independence, or the relevant error-reduction quantities). Consequently the theory does not underwrite the empirical claims.
  2. [Algorithm 1 and §4] Algorithm 1 and §4: the meta-algorithm is motivated by the theoretical conditions, but without evidence that the conditions hold on the control and combinatorial instances, it is unclear whether the observed improvements stem from the stated mechanism or from generic regularization or ensemble effects.
minor comments (2)
  1. [§2 and experimental setup] Notation for the two views is introduced without an explicit table comparing the state-action representations used in each experimental domain.
  2. [Abstract] The abstract claims validation 'across a wide range of tasks' but does not list the precise environments or problem sizes; a compact table would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on strengthening the link between the theoretical conditions and the empirical evaluation. We address each major comment below and will revise the manuscript to incorporate additional analysis and controls.

read point-by-point responses

  1. Referee: [§3 and experimental sections] §3 (sufficient conditions): the manuscript states conditions under which two views permit mutual improvement, yet the experimental sections provide no verification that any evaluated task satisfies these conditions (e.g., no reported measurement of view disagreement, conditional independence, or the relevant error-reduction quantities). Consequently the theory does not underwrite the empirical claims.

    Authors: We agree this is a substantive gap. The sufficient conditions in §3 are presented as motivation for the meta-algorithm rather than as a claim that they hold exactly on every evaluated task. In the revision we will add a new subsection that reports empirical measurements of view disagreement and the relevant error-reduction quantities on the discrete/continuous control and combinatorial optimization tasks. This will allow readers to assess the degree to which the theoretical conditions are approximately satisfied and will clarify the extent to which the observed gains are consistent with the stated mechanism. revision: yes

  2. Referee: [Algorithm 1 and §4] Algorithm 1 and §4: the meta-algorithm is motivated by the theoretical conditions, but without evidence that the conditions hold on the control and combinatorial instances, it is unclear whether the observed improvements stem from the stated mechanism or from generic regularization or ensemble effects.

    Authors: This concern is valid. To isolate the contribution of the co-training procedure, the revised version will include additional ablation studies that compare the full co-training meta-algorithm against (i) single-view baselines, (ii) simple ensembles of independently trained policies, and (iii) regularization-only variants that do not exchange information between views. We will also report the same disagreement and error-reduction metrics on these ablations so that any performance differences can be more directly attributed to the mutual-improvement mechanism described in §3. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper states sufficient conditions under which two-view co-training improves single-view policy learning and motivates a meta-algorithm from those conditions. No equations, fitted parameters, or predictions are exhibited that reduce to the inputs by construction. No self-citations are invoked as load-bearing uniqueness theorems, no ansatzes are smuggled via prior work, and no renaming of known results occurs. The derivation chain is self-contained against external benchmarks because the conditions are presented as independent theoretical statements rather than tautological redefinitions of the algorithm's outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only; the central claim rests on the existence of complementary views and the validity of the (unspecified) sufficient conditions for improvement.

axioms (1)
  • domain assumption Multiple distinct state-action representations exist and supply complementary information for the same underlying decision process.
    Invoked by the co-training setup for sequential decision making.

pith-pipeline@v0.9.0 · 5659 in / 1083 out tokens · 19900 ms · 2026-05-25T10:16:28.603101+00:00 · methodology

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