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arxiv: 2605.09183 · v2 · pith:HABA3NJKnew · submitted 2026-05-09 · 💻 cs.LG

Learning When to Stop: Selective Imitation Learning Under Arbitrary Dynamics Shift

Surbhi Goel , Jonathan Pei , James Wang This is my paper

Pith reviewed 2026-05-20 21:59 UTC · model grok-4.3

classification 💻 cs.LG
keywords selective imitation learningdynamics shiftstopping rulevalidator policieshorizon-free sample complexitybehavior cloningimitation learning
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The pith

A selective imitation learner stops in uncertain states under dynamics shift and achieves horizon-free sample complexity using a small fixed set of validator policies.

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

Standard behavior cloning forces the learner to output an action at every state, which can cause arbitrary performance loss when the test environment has different transitions than the training environment. The paper studies selective imitation, where the learner may stop and avoid acting on states where its demonstrations are uninformative. Given labeled expert trajectories from training and unlabeled state trajectories from the same expert in testing, the learner must produce a policy that rarely stops on training data yet incurs low regret before stopping on test data. The key technical contribution is an algorithm that builds the stopping decision from a validator set whose size stays independent of task length and policy class size. This produces sample complexity that scales only with the logarithm of the policy class size over the accuracy parameter when costs are sparse.

Core claim

The paper establishes that the SeqRejectron algorithm constructs a stopping rule from a validator set of size independent of the horizon and policy class, yielding a selective policy that is complete on the training distribution and sound on the test distribution under arbitrary dynamics shift. For deterministic policies and sparse costs this gives horizon-free sample complexity Õ(log|Π|/ε²). Analogous horizon-free guarantees hold for stochastic policies via a cumulative Hellinger stopping time. The same framework extends to misspecified experts and differing expert policies across environments, with performance degrading gracefully in the amount of misspecification.

What carries the argument

The SeqRejectron algorithm that builds a stopping rule from a small set of validator policies whose cardinality is bounded independently of horizon and policy class size.

If this is right

  • For deterministic policies the sample complexity remains horizon-free and scales as Õ(log|Π|/ε²) under sparse costs.
  • For stochastic policies analogous horizon-free bounds hold through a cumulative Hellinger stopping time.
  • The framework extends to misspecified experts and different expert policies across train and test, with graceful degradation.
  • The validator set size stays independent of horizon and policy class size.

Where Pith is reading between the lines

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

  • The selective stopping mechanism could be paired with a separate fallback policy or human query to handle the states where the learner elects to stop.
  • The validator-based construction may transfer to other sequential tasks that experience gradual distribution shift over long horizons.
  • Empirical tests with controlled amounts of dynamics mismatch could quantify how often the learned policy chooses to stop as a function of shift severity.

Load-bearing premise

The costs are sparse and unlabeled state trajectories from the same expert are available in the test environment.

What would settle it

An experiment or counterexample in which costs have dense support or no unlabeled test trajectories are supplied, causing either the sample complexity to grow with the horizon or the low-regret guarantee before stopping to fail.

Figures

Figures reproduced from arXiv: 2605.09183 by James Wang, Jonathan Pei, Surbhi Goel.

Figure 1
Figure 1. Figure 1: Left: normalized target switched cost and source/target handoff rates as functions of the [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
read the original abstract

Behavior cloning provides strong imitation learning guarantees when training and test environments share the same dynamics. However, in many deployment settings the test environment's transitions differ from training, and classical offline IL offers no recourse: the learner must commit to an action at every state, even when its demonstrations are uninformative and could lead to arbitrary degradation of performance. This motivates the study of selective imitation, where the learner may choose to stop when it cannot act reliably. We introduce a model for selective imitation under arbitrary dynamics shift: given labeled expert demonstrations from a training environment and unlabeled state trajectories from the same expert in a test environment, the learner outputs a selective policy that is complete (rarely stops in training) and sound (incurs low regret before stopping in test). Our algorithm, SeqRejectron, constructs a stopping rule using a small set of validator policies whose size is independent of the horizon or policy class. For deterministic policies, this yields horizon-free $\tilde{O}(\log|\Pi|/\epsilon^2)$ sample complexity, assuming sparse costs. For stochastic policies, we obtain analogous horizon-free guarantees using a cumulative Hellinger stopping time. We extend the framework to misspecified experts and different expert policies across train and test and obtain results that gracefully degrade with the amount of misspecification.

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 introduces a model and algorithm (SeqRejectron) for selective imitation learning under arbitrary train-test dynamics shift. Given expert demonstrations from training and unlabeled state trajectories from the same expert in the test environment, the learner outputs a selective policy that is complete (rarely stops on training data) and sound (low regret before stopping on test data). The algorithm uses a small set of validator policies (size independent of horizon and policy class) to construct a stopping rule. For deterministic policies it claims horizon-free Õ(log|Π|/ε²) sample complexity under sparse costs; for stochastic policies it uses a cumulative Hellinger stopping time. Extensions to misspecified experts and differing train/test expert policies are also provided, with graceful degradation.

Significance. If the derivations and bounds hold, the work offers a principled way to handle arbitrary dynamics shift in imitation learning without committing to actions in uninformative states. The horizon-free sample complexity (conditional on sparse costs) and validator construction independent of horizon are technically notable strengths for long-horizon settings. The framework's extensions to misspecification add practical value, and the emphasis on both completeness and soundness provides clear, falsifiable guarantees.

major comments (2)
  1. [abstract and §4] The horizon-free Õ(log|Π|/ε²) bound for deterministic policies is stated to hold under the sparse-costs assumption (abstract and §4). The manuscript should explicitly derive or cite the step where sparsity prevents pre-stopping regret from scaling linearly with H under arbitrary shift; without this, the stopping-time regret bound appears to reintroduce horizon dependence, undermining the central claim.
  2. [§5] The soundness guarantee for the validator-based stopping rule (SeqRejectron) relies on unlabeled test trajectories from the expert. The paper should clarify whether the sample complexity remains horizon-free if these trajectories are unavailable or if the test expert policy differs substantially from training, as the extension in §5 appears to degrade only under the same sparsity premise.
minor comments (2)
  1. [§3] Notation for the validator set size and its independence from H and |Π| should be introduced earlier (e.g., before the main theorem) to improve readability.
  2. [§2] The abstract mentions 'sparse costs' without a formal definition; add a precise statement (e.g., per-step cost zero except on a small-measure set) in the model section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address each major comment below and indicate planned revisions to strengthen the clarity of the claims.

read point-by-point responses

  1. Referee: [abstract and §4] The horizon-free Õ(log|Π|/ε²) bound for deterministic policies is stated to hold under the sparse-costs assumption (abstract and §4). The manuscript should explicitly derive or cite the step where sparsity prevents pre-stopping regret from scaling linearly with H under arbitrary shift; without this, the stopping-time regret bound appears to reintroduce horizon dependence, undermining the central claim.

    Authors: We agree that an explicit derivation is needed for full transparency. Under the sparse-costs assumption, the analysis in the proof of the main theorem for deterministic policies bounds the pre-stopping regret by showing that costs are incurred only on a measure-zero or low-probability set of states; combined with the validator-based stopping rule, this ensures the accumulated regret before stopping remains independent of H even under arbitrary dynamics shifts. We will add a dedicated lemma and step-by-step derivation in the revised §4 (with a forward reference from the abstract) to make this explicit and cite the sparsity lemma directly. revision: yes

  2. Referee: [§5] The soundness guarantee for the validator-based stopping rule (SeqRejectron) relies on unlabeled test trajectories from the expert. The paper should clarify whether the sample complexity remains horizon-free if these trajectories are unavailable or if the test expert policy differs substantially from training, as the extension in §5 appears to degrade only under the same sparsity premise.

    Authors: The framework is defined to require unlabeled test trajectories from the expert for constructing the validator set and stopping rule; without them the algorithm cannot be executed as stated, so we make no horizon-free claim in that setting. For differing train/test expert policies, §5 already shows graceful degradation of the bounds while retaining horizon-freeness under sparsity. We will add an explicit clarifying paragraph in §5 and the discussion section stating the necessity of test trajectories and confirming that horizon-freeness holds only under the stated assumptions including sparsity. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on explicit assumptions and standard concentration

full rationale

The paper's central result (horizon-free Õ(log|Π|/ε²) sample complexity for deterministic policies) is stated to hold under the explicit assumption of sparse costs. The SeqRejectron algorithm constructs a stopping rule from a fixed-size set of validator policies, with the bound following from this construction plus standard concentration inequalities. No quoted step reduces a prediction to a fitted input by construction, nor does any load-bearing claim rest on a self-citation chain or self-definitional loop. The sparsity premise is introduced as an assumption that enables the horizon-free property rather than being smuggled in via prior work or renaming. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the sparse-costs assumption for the deterministic bound and on the availability of unlabeled expert trajectories in the test environment; no free parameters or new invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Sparse costs assumption for deterministic policies
    Invoked to obtain the horizon-free sample complexity bound.
  • domain assumption Availability of unlabeled state trajectories from the expert in the test environment
    Required to construct the stopping rule and soundness guarantee.

pith-pipeline@v0.9.0 · 5760 in / 1374 out tokens · 64843 ms · 2026-05-20T21:59:54.123022+00:00 · methodology

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