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arxiv: 1907.07238 · v1 · pith:USTJH3TAnew · submitted 2019-07-16 · 💻 cs.RO · cs.LG

Leveraging Experience in Lazy Search

Mohak Bhardwaj , Sanjiban Choudhury , Byron Boots , Siddhartha Srinivasa This is my paper

Pith reviewed 2026-05-24 20:45 UTC · model grok-4.3

classification 💻 cs.RO cs.LG
keywords lazy searchmotion planningimitation learningedge evaluationgraph searchroboticsMDP
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The pith

A policy learned by imitating oracular edge selectors solves similar motion planning problems with fewer edge evaluations.

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

The paper establishes that lazy graph search for motion planning can be accelerated by learning an edge evaluation ordering from prior experience. It formulates selector choice as an MDP on the search state and trains a policy by imitating oracles that know the optimal ordering on training problems. A sympathetic reader would care because edge evaluation, typically a collision check, dominates runtime, and a learned ordering that invalidates bad paths early reduces the total number of checks. If new problems are similar enough to the training distribution, the policy transfers without hand-crafted heuristics.

Core claim

Lazy search defers edge evaluations by repeatedly finding the shortest potentially feasible path and checking its edges until a feasible path is confirmed. The central claim is that oracular selectors, which solve the MDP optimally on training instances, can supervise an imitation learning procedure that produces a policy effective on new instances drawn from a similar distribution, thereby minimizing the cumulative number of edge evaluations required.

What carries the argument

MDP on the state of the search problem, solved during training by oracular selectors and transferred via imitation learning to a runtime policy for edge ordering.

If this is right

  • The learned selector outperforms commonly used heuristics on a range of 2D and 7D motion planning problems when the similarity condition holds.
  • A good edge ordering both identifies invalid edges quickly and removes many future candidate paths from consideration.
  • Formulating selection as an MDP makes the problem amenable to imitation learning once oracles are available.
  • Solving the large MDP exactly is intractable, so the oracle-plus-imitation route is required to obtain a usable policy.

Where Pith is reading between the lines

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

  • The same oracle-imitation pipeline could be applied to other search settings where the cost of evaluating actions dominates, such as symbolic planning with expensive precondition checks.
  • Collecting experience from deployed robots would allow the policy to improve continuously as the robot encounters new but related environments.
  • If similarity breaks down, an online adaptation mechanism that fine-tunes the policy on recently solved problems could restore performance without full retraining.

Load-bearing premise

New search problems must be sufficiently similar to the problems solved during training.

What would settle it

Apply the learned policy to a test set of motion planning problems drawn from a distribution clearly different from the training distribution and check whether the number of edge evaluations exceeds that of standard heuristics.

Figures

Figures reproduced from arXiv: 1907.07238 by Byron Boots, Mohak Bhardwaj, Sanjiban Choudhury, Siddhartha Srinivasa.

Figure 1
Figure 1. Figure 1: The LAZYSP [2] framework. LAZYSP iteratively computes the shortest path, queries a SELECTOR for an edge on the path, evaluates it and updates the graph until a feasible path is found. The number of edges evaluated depends on the choice of SELECTOR. We propose to train a SELECTOR from prior data. (verify if they are valid) and return a path ξ ∗ upon halting. Two conditions must be met: 1) The returned path … view at source ↗
Figure 2
Figure 2. Figure 2: Overview of STROLL- a training procedure for a SELECTOR to select edges to evaluate in the LAZYSP framework. In each training iteration, a world map φ is sampled. The learner is executed upto a time step to get a state st which is the set of edges evaluated and their outcomes. The learner has to decide which edge to evaluate on the current shortest path. It extracts features from every edge - we use a set … view at source ↗
Figure 3
Figure 3. Figure 3: Distribution over worlds for (a) Environment 1 and (b) Environment [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average reward per epsiode of Tabular Q-learning. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Edges evaluated (green valid, red invalid) on a world from B [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) STROLL-R (green) vs STROLL (orange) (b) Densification of data. (a) (b) 0 25 50 75 100 125 150 175 Training Episodes -20 -40 -60 -80 -100 -120 -140 -160 Average Rewards 0 20 40 60 80 100 -40 -50 -60 -70 -80 -90 -100 -110 -120 Rewards Percentage Mixing StrOLL Q-Learning StrOLL Alternate [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Running average reward for 200 episodes of training. Q learning [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Weight bins depicting relative importance of each feature learned by the learner. S [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

Lazy graph search algorithms are efficient at solving motion planning problems where edge evaluation is the computational bottleneck. These algorithms work by lazily computing the shortest potentially feasible path, evaluating edges along that path, and repeating until a feasible path is found. The order in which edges are selected is critical to minimizing the total number of edge evaluations: a good edge selector chooses edges that are not only likely to be invalid, but also eliminates future paths from consideration. We wish to learn such a selector by leveraging prior experience. We formulate this problem as a Markov Decision Process (MDP) on the state of the search problem. While solving this large MDP is generally intractable, we show that we can compute oracular selectors that can solve the MDP during training. With access to such oracles, we use imitation learning to find effective policies. If new search problems are sufficiently similar to problems solved during training, the learned policy will choose a good edge evaluation ordering and solve the motion planning problem quickly. We evaluate our algorithms on a wide range of 2D and 7D problems and show that the learned selector outperforms baseline commonly used heuristics.

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

3 major / 2 minor

Summary. The paper formulates edge selection ordering in lazy graph search for motion planning as an MDP on the search state. It computes oracular selectors during training and applies imitation learning to obtain policies. The central claim is that, when new problems are sufficiently similar to those seen in training, the learned policy selects an effective ordering and solves instances faster than standard heuristics; this is supported by reported outperformance on a range of 2D and 7D problems.

Significance. If the generalization claim holds, the work offers a practical way to leverage prior experience to reduce edge evaluations, a key bottleneck in lazy planning. The oracle-based imitation learning approach is a clear strength, as it supplies high-quality training signals without requiring the policy to be defined circularly. The method could influence experience-driven planning pipelines in robotics, provided the similarity assumption can be made operational.

major comments (3)
  1. [Abstract and §5] Abstract and §5 (Experiments): the reported outperformance on 2D/7D problems supplies no error bars, confidence intervals, or statistical tests comparing the learned selector against baselines, so the magnitude and reliability of the improvement cannot be assessed.
  2. [Abstract and §4] Abstract (final paragraph) and §4 (MDP and policy): the transfer claim is conditioned on 'sufficiently similar' problems, yet no metric, embedding distance, or distribution-shift experiment is defined or performed; without this, it is impossible to separate genuine generalization from memorization of the training distribution.
  3. [§5] §5 (Experiments): no train/test split protocol, cross-validation procedure, or ablation on deliberately dissimilar instances is described, leaving the central generalization assumption untested and load-bearing for the main result.
minor comments (2)
  1. [§4] The abstract states that oracles are 'computed externally' but the manuscript never specifies the exact procedure or computational cost of obtaining them; a short paragraph in §4 would clarify this.
  2. [§3] Notation for the state representation and similarity function is introduced without an explicit equation or pseudocode block, making the MDP definition harder to follow on first reading.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments correctly identify gaps in the experimental reporting and the need to better substantiate the generalization claim. We address each point below and will make the corresponding revisions.

read point-by-point responses

  1. Referee: [Abstract and §5] Abstract and §5 (Experiments): the reported outperformance on 2D/7D problems supplies no error bars, confidence intervals, or statistical tests comparing the learned selector against baselines, so the magnitude and reliability of the improvement cannot be assessed.

    Authors: We agree. The original results reported only mean performance. In the revision we will add per-problem standard deviations across repeated runs with different random seeds and include statistical comparisons (paired Wilcoxon tests) between the learned policy and each baseline. revision: yes

  2. Referee: [Abstract and §4] Abstract (final paragraph) and §4 (MDP and policy): the transfer claim is conditioned on 'sufficiently similar' problems, yet no metric, embedding distance, or distribution-shift experiment is defined or performed; without this, it is impossible to separate genuine generalization from memorization of the training distribution.

    Authors: The manuscript states the claim conditionally. We acknowledge that the absence of a quantitative similarity measure leaves the generalization claim under-supported. We will add to §4 a concrete similarity metric based on the Wasserstein distance between obstacle-position distributions and will include a controlled distribution-shift experiment in the revised §5. revision: yes

  3. Referee: [§5] §5 (Experiments): no train/test split protocol, cross-validation procedure, or ablation on deliberately dissimilar instances is described, leaving the central generalization assumption untested and load-bearing for the main result.

    Authors: We will revise §5 to document the exact train/test generation procedure (distinct seeds, same parametric family) and add an explicit ablation that systematically increases dissimilarity (number and placement of obstacles) while measuring degradation of the learned policy relative to the oracle. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation is self-contained imitation learning from external oracles

full rationale

The paper defines an MDP on search state, computes oracular selectors externally to solve the MDP at training time, then applies imitation learning to obtain a policy. This chain does not reduce any quantity to itself by definition, nor does it rename a fitted parameter as a prediction, nor rely on self-citation for a uniqueness claim. The conditional statement about similarity to training problems is an explicit generalization assumption rather than a tautological step. No load-bearing equation or premise collapses to its own input.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the ability to compute oracular selectors during training and on the transferability of the learned policy under a similarity assumption between training and test problems. No explicit free parameters or invented entities are named in the abstract.

axioms (1)
  • domain assumption The state of the lazy search problem can be modeled as an MDP whose actions correspond to edge evaluations.
    Abstract states: 'We formulate this problem as a Markov Decision Process (MDP) on the state of the search problem.'

pith-pipeline@v0.9.0 · 5729 in / 1247 out tokens · 21565 ms · 2026-05-24T20:45:53.691238+00:00 · methodology

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Reference graph

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