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TeachMyAgent: a Benchmark for Automatic Curriculum Learning in Deep RL

Clément Romac, Rémy Portelas, Katja Hofmann, Pierre-Yves Oudeyer

arXiv:2103.09815v2cs.LG

TL;DR

ACL has demonstrated advantages over random task sampling across diverse experimental setups, including sim2real robotics, video games, and procedurally generated navigation. TeachMyAgent combines challenge-specific procedural Box2D unit tests, a procedural Parkour environment, diverse DRL students, and representative ACL algorithms. Current ACL approaches without expert knowledge match and can outperform knowledge-intensive methods, while the Parkour environment remains far from solved.

  • Problem

    ACL has demonstrated advantages over random task sampling across diverse experimental setups, including sim2real robotics, video games, and procedurally generated navigation.

    Source: §1 · p. 2

  • Method

    TeachMyAgent combines challenge-specific procedural Box2D unit tests, a procedural Parkour environment, diverse DRL students, and representative ACL algorithms.

    Source: §1 · pp. 2–3

  • Results

    Current ACL approaches without expert knowledge match and can outperform knowledge-intensive methods, while the Parkour environment remains far from solved.

    Source: §7 · p. 8

  • Takeaways & Limitations

    TeachMyAgent provides an open benchmark and baseline suite for multidimensional ACL comparisons and future method development.

    Source: §1 · p. 3

    The study focuses on single-agent generalist DRL with given, relatively low-dimensional continuous task spaces and 2D locomotion environments.

    Source: §7 · p. 9

Abstract

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Training autonomous agents able to generalize to multiple tasks is a key target of Deep Reinforcement Learning (DRL) research. In parallel to improving DRL algorithms themselves, Automatic Curriculum Learning (ACL) study how teacher algorithms can train DRL agents more efficiently by adapting task selection to their evolving abilities. While multiple standard benchmarks exist to compare DRL agents, there is currently no such thing for ACL algorithms. Thus, comparing existing approaches is difficult, as too many experimental parameters differ from paper to paper. In this work, we identify several key challenges faced by ACL algorithms. Based on these, we present TeachMyAgent (TA), a benchmark of current ACL algorithms leveraging procedural task generation. It includes 1) challenge-specific unit-tests using variants of a procedural Box2D bipedal walker environment, and 2) a new procedural Parkour environment combining most ACL challenges, making it ideal for global performance assessment. We then use TeachMyAgent to conduct a comparative study of representative existing approaches, showcasing the competitiveness of some ACL algorithms that do not use expert knowledge. We also show that the Parkour environment remains an open problem. We open-source our environments, all studied ACL algorithms (collected from open-source code or re-implemented), and DRL students in a Python package available at https://github.com/flowersteam/TeachMyAgent.

1. Introduction

TeachMyAgent addresses the difficulty of comparing ACL algorithms by identifying distinct teaching challenges and introducing a procedural benchmark with unit tests, Parkour, diverse students, and comparative baselines.

Motivation

  • Existing ACL comparisons are difficult because studies vary in expert knowledge, evaluation targets, baselines, and DRL students.A unified benchmark with shared baselines is proposed to reduce these comparison barriers.Source: §1 · p. 2

Benchmark and contributions

  • TeachMyAgent introduces a benchmark combining challenge-specific procedural Box2D unit tests with a Parkour environment for global ACL assessment.The benchmark includes diverse embodiments and DRL students, including random black-box student scenarios.Source: §1 · pp. 2–3

Teaching challenges

  • ACL methods must handle mostly unfeasible spaces, mostly trivial spaces, catastrophic forgetting, diverse students, rugged difficulty landscapes, and limited expert knowledge.These challenges require teachers to detect promising subspaces, preserve skills, adapt across students, and navigate discontinuous task difficulty.Source: §1 · p. 2

Scope

  • TeachMyAgent focuses on continuous, relatively low-dimensional task spaces for single-agent generalist DRL, excluding discrete tasks, multi-agent settings, and learned task representations.These exclusions define the benchmark’s intended scope rather than a general evaluation of all ACL settings.Source: §1 · p. 3

Study and outcome

  • The benchmark compares representative ACL approaches through unit tests and global assessments, finding expert-knowledge-free methods competitive while Parkour remains largely unsolved.The study also releases environments, algorithms, students, baselines, tutorials, and reproducibility scripts.Source: §1 · p. 3

2. Related work

TeachMyAgent differs from DRL benchmarks by evaluating teacher algorithms that organize curricula over controllable procedural task spaces rather than learning architectures or randomly presented tasks.

Relation to DRL benchmarks

  • Existing DRL suites such as Atari, DeepMind Lab, TextWorld, BabyAI, and bsuite primarily benchmark agents learning in fixed or randomly presented environments.TeachMyAgent instead targets efficient curriculum generation across a parametric task space.Source: §2 · p. 3

Benchmark objective

  • TeachMyAgent optimizes how a teacher organizes curricula for a given task space and DRL student, rather than developing more efficient learning architectures.Its objective is to maximize student performance over the task set through curriculum generation.Source: §2 · pp. 3–4

Procedural generation

  • Unlike Procgen’s uncontrollable random generation, TeachMyAgent controls procedural-generation parameters so ACL methods can select tasks directly.The paper identifies adapting Procgen for direct procedural control as future work.Source: §2 · p. 4

ACL benchmarking gap

  • Earlier ACL studies used heterogeneous environments, comparisons, and evaluation targets, motivating an in-depth benchmark with multiple unit tests and shared baselines.TeachMyAgent extends procedural Box2D ACL work with broader comparative analysis and open-source environments.Source: §2 · p. 4

3. ACL baselines

The paper formalizes ACL as learning a task-distribution policy from interaction history, categorizes expert knowledge, and compares seven representative teachers plus random sampling.

Framework

  • ACL learns a function mapping information retained from past task-space interactions to a distribution of tasks for the DRL student.The objective concerns post-training performance over test tasks after a fixed episodic budget, though surrogate objectives are commonly used.Source: §3 · p. 4

Expert knowledge

  • The benchmark classifies expert knowledge as initial task distributions, target task distributions, or reward ranges identifying mastered tasks.This taxonomy connects available prior knowledge to ACL method selection.Source: §3 · p. 4

Implemented baselines

  • Seven ACL methods span learning-progress, neural task-generation, and distribution-shifting approaches, with uniform random task selection as a baseline.The methods are RIAC, Covar-GMM, ALP-GMM, Goal-GAN, Setter-Solver, ADR, and SPDL.Source: §3 · p. 4

4. The TeachMyAgent benchmark

TeachMyAgent combines procedural Box2D environments, diverse embodied DRL learners, and ACL-specific task spaces to support systematic benchmarking. Its environments range from interpretable Stump Tracks unit tests to the richer, embodiment-dependent Parkour space.

4. The TeachMyAgent benchmark

  • TeachMyAgent defines experiments by combining an ACL method, a procedural environment, and an embodied DRL learner.The benchmark provides two procedural Box2D environments, multiple morphologies, and SAC and PPO learners.Source: §4 · p. 5, §4.2 · p. 5

4.1. Environments

  • Stump Tracks uses a low-dimensional procedural task space controlling stump height and spacing, enabling visualizable ACL unit-test variants.The walker receives continuous torque actions and lidar-, position-, and joint-based observations, with forward-progress and torque-use rewards.Source: §4.1 · p. 5, Figure 2 · p. 5
  • Parkour generates uneven terrains with a fixed CPPN, creepers, and water across a rich task space whose optimal curriculum depends on the agent’s embodiment.Its CPPN input, creeper parameters, and water level form a six-dimensional task space with rugged difficulty.Source: §4.1 · p. 5

4.2. Learners

  • The benchmark includes walking, swimming, climbing, and other morphologies so ACL methods can be evaluated across different locomotion demands.Provided learners include short and quadrupedal walkers, fish, chimpanzee, spider, and millipede embodiments.Source: §4.2 · p. 5
  • SAC and PPO provide distinct off-policy and on-policy DRL student algorithms for benchmarking ACL teachers.SAC optimizes reward and action entropy, whereas PPO uses approximate trust-region gradient updates.Source: §4.2 · p. 5

5. Experiments

The experiments evaluate ACL methods through challenge-specific Stump Tracks unit tests and a global Parkour benchmark under controlled training and testing procedures. Expert-knowledge-free methods are competitive, but Parkour remains difficult, with performance varying sharply by method and embodiment.

5.1. Experimental details

  • The benchmark trains students for 20 million steps and evaluates the percentage of 100 test tasks mastered, using reward above 230 and Welch’s t-tests for comparisons.Teachers sample procedural task parameters each episode, and testing occurs every 500,000 steps.Source: §5.1 · p. 6

5.2. Challenge-specific comparison with Stump Tracks

  • The challenge-specific study varies task feasibility, triviality, student forgetting, student diversity, ruggedness, and expert-knowledge availability to isolate ACL capabilities.The five Stump Tracks variants include nearly 80% unfeasible tasks, 50% newly trivial tasks, model resets, multiple embodiments and learners, and scattered feasible tasks.Source: §5.2 · p. 6
  • Across 15 Stump Tracks experiments, expert-knowledge-free methods achieve similar final performance with and without expert knowledge, although prior knowledge improves sample efficiency.These experiments cover five challenges under three expert-knowledge conditions.Source: §5.2 · pp. 6–7
  • With low expert knowledge, ADR is not significantly different from Random in all challenges and GoalGAN beats Random only in mostly trivial spaces; with high knowledge, both reach the top three on 3/5 challenges.The contrast exposes dependence on an initial easy-task distribution.Source: §5.2 · p. 7
  • ADR performs worse on rugged difficulty and GoalGAN on student forgetting, while their mechanisms respectively become stuck in hard subspaces and update too slowly.ADR’s expansion can stall in infeasible regions, whereas GoalGAN’s buffer and GAN updates create inertia.Source: §5.2 · pp. 6–8
  • SPDL is significantly inferior to Random in 11/15 experiments because it optimizes a Gaussian target distribution while evaluation uses uniformly sampled tasks.This reveals sensitivity to mismatch between the teacher’s optimized distribution and the benchmark test distribution.Source: §5.2 · pp. 6, 8

5.3. Global performance analysis using the Parkour

  • Parkour remains an open challenge: expert-knowledge-free methods perform best overall, while climbing reaches at most 1% mastered tasks and other morphologies remain low and variable.Bipedal-walker performance stays below 60% and fish performance below 50%, despite feasible test tasks.Source: §5.3 · p. 8

6. Open-Source release of TeachMyAgent

TeachMyAgent is released as an extensible open-source package containing its environments, embodiments, DRL students, ACL implementations, experiment-reproduction code, and benchmark results.

6. Open-Source release of TeachMyAgent

  • The release provides APIs for adding ACL methods, learning algorithms, embodiments, and environments, alongside reproducible experiments and precomputed benchmark results.Jupyter notebooks generate the paper’s figures, and stored results enable baseline comparisons without rerunning large-scale experiments.Source: §6 · p. 8

7. Discussion and Conclusion

TeachMyAgent benchmarks ACL methods with unit tests and the challenging Parkour environment, where current teachers still struggle to identify feasible task subspaces. The study finds that methods without expert knowledge can match or outperform knowledge-heavy approaches, while Parkour remains far from solved.

7. Discussion and Conclusion

  • Methods without expert knowledge matched or outperformed approaches using high amounts of expert knowledge, while Parkour remained far from solved.The authors identify ALP-GMM as an example of a no-expert-knowledge method achieving this competitiveness.Source: §7 · p. 8
  • TeachMyAgent combines challenge-specific unit-test environments with Parkour, a difficult teaching scenario for assessing ACL algorithms.The benchmark uses unit tests for core skills and Parkour for global performance assessment.Source: §7 · pp. 8–9
  • Figure 4 reports averaged Parkour performance over 48 seeds and marks results statistically different from Random every 5 million steps.Statistical differences use p < 0.05, with standard error of the mean shown.Source: Figure 4 · p. 9
  • The benchmark remains limited to low-dimensional procedural-generation systems and primarily 2D locomotion tasks.The authors propose higher-dimensional procedural generation and additional environments such as ProcGen or robotic manipulation.Source: §7 · p. 9
  • Future extensions include environment-conditioned goal selection and using TeachMyAgent to study Meta ACL across sequences of students.These extensions would broaden the benchmark beyond its current task-selection setting.Source: §7 · p. 9

A. Details on ACL baselines

  • The baseline implementation section documents ACL algorithms and their hyperparameter tuning procedures.This material supports reproducible comparisons but is not itself a substantive conclusion of the discussion.Source: A. Details on ACL baselines · p. 13

A.1. Implementation details

The benchmark implements diverse ACL teachers using task distributions, learning progress, goal generation, feasibility prediction, or adaptive distribution shifts. It tunes these methods on Stump Tracks and evaluates them across procedural locomotion environments including Parkour.

A.1. Implementation details

  • ADR begins from an easy-centered task distribution and expands or contracts its boundaries using episodic-reward buffers and thresholds.Boundary updates are applied dimension by dimension, with buffer averages compared against lower and upper thresholds.Source: §A.1 · p. 13
  • RIAC recursively splits task-space regions by differences in learning progress, whereas Covar-GMM selects Gaussian components according to learning progress while retaining random exploration.Covar-GMM fits mixtures using recent tasks, time, and competence, with a random-sampling probability.Source: §A.1 · pp. 13–14
  • ALP-GMM estimates per-task absolute learning progress, fits a recent-task GMM, and samples from Gaussians with high mean learning progress without expert knowledge.It uses a k-nearest-neighbor history-based estimate and periodically refits the GMM.Source: §A.1 · p. 14
  • GoalGAN generates intermediate-difficulty tasks with a GAN trained from binary success labels, using reward thresholds and a replay buffer to preserve previously found goals.It can also pretrain the generator with positive tasks from an initial Gaussian distribution.Source: §A.1 · p. 14
  • SPDL shifts a Gaussian task distribution toward a target by maximizing student performance while penalizing KL divergence and limiting each update’s distributional shift.Its implementation was not well matched to uniformly sampled Stump Tracks because the Gaussian target differed from the test distribution.Source: §A.1 · p. 15
  • Setter-Solver uses a Judge and Setter to generate feasible, diverse tasks, but this benchmark omits its conditioned and target-distribution variants.The omitted variants were left for future work, although the targeted version reportedly improves sample efficiency with similar final results.Source: §A.1 · pp. 15–16

A.2. Hyperparameters tuning

  • Hyperparameters were selected through grid search on Stump Tracks using 7 million steps and 16 seeds, with roughly 70 sampled configurations per teacher.The best configuration was chosen by average mastered-task percentage at training end, following original-paper recommendations and expert-knowledge settings.Source: §A.2 · p. 16

B.2. Parkour

  • Parkour procedurally generates uneven terrain with fixed CPPN architecture and weights, creating a rugged task-space difficulty landscape that requires extensive exploration.The environment extends the Stump Tracks setting with neural-network-generated terrain and multiple task-space variants.Source: §B.2 · p. 18

B.2.1. PROCEDURAL GENERATION

Parkour procedurally generates diverse, rugged tasks through CPPN-based terrain, creepers, and water, while adapting physics, observations, actions, and morphologies to different embodiments.

B.2.1. PROCEDURAL GENERATION

  • CPPN terrain generation maps a three-dimensional parameter vector to nonlinear ground and ceiling functions, producing diverse terrains and a rugged difficulty landscape.The fixed four-layer network also permits ground-ceiling crossings that create unfeasible tasks; smoothing uses δ = 10 during training.Source: §B.2.1 · pp. 18–19
  • Parkour adds creepers and water as task-space dimensions, enabling graspable structures and simplified aquatic physics.Creepers can form rotating-joint climbing objects, while water introduces buoyancy, drag, lift, and push forces.Source: §B.2.1 · p. 20, §B.2.2 · p. 20

B.2.2. PHYSICS

  • Embodiment-specific survival rules require teachers to place swimmers, climbers, and walkers in compatible milieus.Swimmers die after prolonged time outside water, whereas climbers and walkers cannot survive underwater for more than 600 consecutive steps.Source: §B.2.2 · p. 21

B.2.3. OBSERVATION AND ACTION SPACE

  • The observation vector has 26 morphology-independent features covering lidar detections, water and death status, body state, and grasping contacts.Lidars additionally encode whether detected objects are water, creepers, or neither, and climbers receive sensor-grasp actions in [-1; 1].Source: §B.2.3 · p. 21

B.3. Morphologies

  • The benchmark spans walkers, climbers, swimmers, and an amphibious walker, with morphology-specific bodies, sensors, densities, and capabilities.Provided embodiments include classic, short, quadrupedal, spider, millipede, chimpanzee-like, fish-like, and amphibious agents.Source: §B.3 · pp. 21–22

C.2. General experimental setup

Each experiment trains a DRL student while an ACL teacher selects procedural tasks at episode resets, then evaluates generalization on fixed test tasks and monitors curriculum evolution.

C.2. General experimental setup

  • Teachers select a new task vector at every environment reset during 20 million student steps and receive episodic or binary reward feedback.SPDL additionally receives per-step rewards and initial states, whereas GoalGAN and Setter-Solver can use binary reward signals.Source: §C.2 · p. 23
  • Student performance is tested every 500,000 steps on 100 predefined tasks, while training-task rewards and sampled curricula are monitored separately.Monitoring samples are collected every 250,000 steps without perturbing teacher buffers.Source: §C.2 · pp. 23–24
  • The full benchmark is computationally demanding: all skill-specific and Parkour experiments require approximately 4776 GPU hours.The estimate corresponds to 4608 GPU hours for skill-specific experiments and 168 GPU hours for Parkour.Source: §C.2 · p. 24

C.3. Stump Tracks variants

  • The benchmark’s Stump Tracks comparison uses six challenge-specific variants, 32 seeds per experiment, and a shared 100-task test set.The common test set is evenly distributed over μ_s ∈ [0; 3] and Δ_s ∈ [0; 6].Source: §C.3 · p. 24, §C.3.1 · p. 24

C.3.2. EXPERIMENTS

The Stump Tracks experiments isolate ACL challenges by manipulating task-space difficulty, student forgetting, expert-knowledge access, and student diversity under controlled comparisons.

C.3.2. EXPERIMENTS

  • Expert-knowledge comparisons provide no, low, or high prior knowledge, changing access to reward mastery ranges, initial regions, and task-space distributions.The no-knowledge setup still supplies randomly centered initial and Gaussian target distributions, while high knowledge initializes teachers near trivial tasks.Source: §C.3.2 · pp. 24–25
  • The no-expert setup’s Gaussian target distribution is not close enough to the uniform test distribution for SPDL to form an efficient curriculum.The authors state that matching the true test distribution would require modifying the target distribution.Source: §C.3.2 · p. 24
  • The mostly unfeasible condition sets stump height means over [0; 9], making almost 80% of tasks infeasible for the classic bipedal walker.The setup assumes heights greater than 3 are impossible for that embodiment.Source: §C.3.2 · p. 25
  • The benchmark creates challenge-specific variants for mostly trivial, mostly unfeasible, rugged, forgetting, and diverse-student conditions.The rugged variant cuts and shuffles task-space regions, creating discontinuities, peaks, and cliffs in difficulty.Source: §C.3.2 · pp. 25–26
  • Robustness is aggregated across PPO and SAC students paired with short-bipedal and spider embodiments over 128 seeds.The four constituent experiments each use 32 seeds.Source: §C.3.2 · p. 26

C.4. Parkour experiments

Parkour evaluation uses embodiment-specific task spaces and test sets to assess learning across feasible, difficult, and out-of-distribution procedural environments.

C.4. Parkour experiments

  • The Parkour experiment uses 48 seeds across classic bipedal, chimpanzee, and fish embodiments, with a bounded three-dimensional CPPN input space.The medium space is θ ∈ [−0.35, 0.05] × [0.6, 1.0] × [−0.1, 0.3].Source: §C.4 · p. 26
  • Easy, medium, and hard CPPN spaces differ in feasible-task ratios while preserving diverse terrains within their respective bounds.The easy and medium spaces were designed from the hard space and their boundaries were selected to contain feasible tasks.Source: §C.4 · p. 26

C.4.1. TEST SETS

  • Each embodiment receives a separate 100-task test set containing one-third easy, medium, and hard tasks, with 40 tasks outside the training task space.The remaining 60 tasks belong to the training space, and all tasks were hand-designed to match the morphology’s physical capabilities.Source: §C.4.1 · pp. 26–27, Figure 7 · p. 27

D. Additional results

  • The broader evaluation tracks mastered-task percentages from episodic rewards above 230 and reports seed-level statistical comparisons using Welch’s t-test.Performance is monitored on test tasks and training tasks every 500,000 student steps.Source: D. Additional results · p. 28

D.1. Original Stump Tracks

  • Original Stump Tracks results average performance over 32 seeds and use the best prior-knowledge configuration as an upper baseline for challenge comparisons.Table 3 reports the percentage of mastered tasks after 20 million steps on 100 evenly distributed tasks.Source: §D.1 · p. 28, Table 3 · p. 28

D.2.1. OVERALL RESULTS

The study evaluates each ACL teacher after 20 million training steps across challenge-specific experiments, using tables and pairwise statistical comparisons to assess performance differences.

D.2.1. OVERALL RESULTS

  • After 20 million steps, performance is reported for every ACL teacher and challenge, with averages and standard deviations shown under no, low, and high prior knowledge.Figure 8 complements these results with pairwise Welch’s t-tests for every challenge.Source: §D.2.1 · p. 28, Table 4 · p. 29, Table 5 · p. 29

D.2.2. CASE STUDY: SAMPLE EFFICIENCY

The case studies show that expert knowledge and task-space structure strongly affect ACL sample efficiency, recovery from forgetting, and final performance. They also identify concrete failure modes for GoalGAN, SPDL, and ADR.

D.2.2. CASE STUDY: SAMPLE EFFICIENCY

  • After 5 million steps, ALP-GMM and high-knowledge ADR can reach twice Random’s performance in mostly unfeasible spaces, whereas curriculum learning matters less in mostly trivial spaces.Rugged landscapes remain difficult to explore within this short training budget.Source: §D.2.2 · p. 31, Figure 9 · p. 32
  • High expert knowledge makes ADR and GoalGAN nearly reach their 20-million-step performance after 5 million steps, while GoalGAN is best in 3/5 challenges under that setup.Adding expert knowledge also improves ALP-GMM’s bootstrapping by focusing it on feasible regions.Source: §D.2.2 · p. 31, Figure 9 · p. 32

D.2.3. CASE STUDY: ON THE DIFFICULTY OF GOALGAN AND SPDL TO ADAPT THE CURRICULUM TO FORGETTING STUDENTS

  • After student resets, ADR and ALP-GMM quickly recover and improve, whereas GoalGAN and SPDL fail to recover, producing poor final performance.SPDL’s shift toward a target distribution may hinder reversal to simpler tasks, while GoalGAN’s intermediate-difficulty buffer becomes obsolete after resets.Source: §D.2.3 · pp. 32–33, Figure 10 · p. 33

D.2.4. CASE STUDY: IMPACT OF EXPERT KNOWLEDGE ON ALP-GMM

  • High expert knowledge significantly improves ALP-GMM early in both mostly unfeasible and forgetting challenges, but the advantage becomes statistically insignificant later.Final results improve in almost all challenges, yet original Stump Tracks results favor no expert knowledge, leaving the whole-training benefit unclear.Source: §D.2.4 · pp. 33–34, Figure 11 · p. 34

D.2.5. CASE STUDY: WHAT ADR NEEDS

  • ADR depends on an initially easy task and a smooth difficulty landscape; it can become stuck when initialized in a hard region or when unfeasible regions interrupt the task space.On the rugged challenge, ADR performs worst, significantly below Random, regardless of expert knowledge.Source: §D.2.5 · p. 35, Figure 12 · p. 35, Figure 13 · p. 36

D.3.1. OVERALL RESULTS

On Parkour, ALP-GMM is the only teacher significantly better than Random throughout training, while ADR eventually underperforms Random. Climbing locomotion remains especially difficult for all evaluated curricula.

D.3.1. OVERALL RESULTS

  • On Parkour, ALP-GMM is the only teacher significantly better than Random throughout training, while ADR plateaus early and eventually performs significantly worse than Random.Covar-GMM remains close to ALP-GMM; RIAC is similar to GoalGAN, and SPDL remains similar to Random.Source: §D.3.1 · p. 36, Figure 14 · p. 37, Table 7 · p. 37
  • Across bipedal-walker and fish experiments, mastered-task percentages are evaluated every 5 million steps against Random using statistical significance tests.The Parkour table aggregates results over 48 seeds, with 16 seeds for each morphology.Source: Table 7 · p. 37, Figure 15 · p. 38, Figure 16 · p. 38

D.3.2. CASE STUDY: LEARNING CLIMBING LOCOMOTION

  • None of the ACL methods enables the chimpanzee student to master more than 1% of the climbing test set.In a simpler CPPN input space without water, Random exceeds 6%, with its best seed reaching 30% after 10 million steps; benchmark performance peaks at 1% for SPDL.Source: §D.3.2 · pp. 38–39, Figure 17 · p. 39, Figure 18 · p. 39

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