Pith. sign in

REVIEW 3 major objections 6 minor 24 references

RL agents find six game exploits on their own in NHL 26

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · glm-5.2

2026-07-09 08:54 UTC pith:EPLDDZDB

load-bearing objection Sequential reward masking finds diverse scoring exploits in NHL 26; the six-exploit match with human playtesters is unverifiable. the 3 major comments →

arxiv 2607.07498 v1 pith:EPLDDZDB submitted 2026-07-08 cs.LG cs.AI

Reward-Adaptive Iterative Discovery: A Case Study on Automated Game Testing for NHL26

classification cs.LG cs.AI
keywords reinforcement learningautomated game testingquality diversityreward maskingexploit discoveryNHL 26goalie AIsequential training
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Reinforcement learning agents, left to their own devices, tend to converge on a single best solution. This paper proposes a method called Reward-Adaptive Iterative Discovery (RAID) that forces RL agents to find multiple distinct high-quality strategies in sequence. The core mechanism is reward masking: after an agent converges on a scoring strategy, the reward function is modified so that future agents receive zero reward for scoring from the same position with the same shot type (within a 2-meter radius). Each subsequent agent must therefore discover a novel way to score. Applied to the goalie AI in NHL 26, RAID found six distinct scoring exploits in a single experiment without human intervention between iterations, and these six matched exploits that human playtesters had previously found through hours of manual testing. The paper compares RAID to a naive baseline of running standard RL 20 times with different random seeds, which consistently produced only two strategies across all runs. RAID produced ten distinct strategies across the same number of iterations. The diversity criterion—shot type plus average shot position—is deliberately domain-specific and interpretable by non-RL practitioners, which the authors argue is a practical advantage over prior diversity methods that require RL expertise to tune.

Core claim

Sequential reward masking is a sufficient mechanism to overcome RL's tendency to collapse to a single optimal solution. By zeroing out reward for previously found strategies (defined by shot type and position within a 2m radius), each new agent is forced to explore a different region of the strategy space. The method is simple enough for non-RL practitioners to configure and use, and it produces exploits comparable to those found by human testers. The paper also documents a key failure mode: agents can learn bi-modal behaviors where shots scatter around two positions, leaving roughly one-third of shots outside the exclusion radius, which means future iterations can still be rewarded for a策略s

What carries the argument

Reward masking: after each agent converges, the reward function is modified to give zero reward for goals scored from within 2m of a previously found average shot position when using the same shot type. This is a hard constraint (binary zero reward) rather than a soft penalty, and it is applied sequentially (one agent at a time) rather than in parallel, which the authors argue increases stability compared to parallel diversity methods that learn diversity representations alongside policies.

Load-bearing premise

The diversity criterion—defining a strategy solely by shot type and average shot position within a 2m radius—is sufficient to force meaningfully different behaviors. An agent can learn bi-modal behavior where shots scatter around two positions, leaving about a third of shots outside the exclusion radius, which means future iterations can still learn substantially the same strategy.

What would settle it

Run RAID on a game where the set of possible exploits is known exhaustively. If the method fails to find a significant fraction of known exploits, or if it repeatedly rediscovers near-identical strategies that evade the diversity criterion (e.g., via multimodality), the core utility claim is weakened.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Game studios could integrate RAID into their CI/CD pipeline to automatically surface goalie AI weaknesses after each behavior update, reducing the manual testing burden.
  • The reward masking approach is domain-agnostic in principle (Algorithm 1) and could be applied to other game testing scenarios beyond hockey scoring, such as fighting game combos or racing line exploits, as long as a domain-specific diversity criterion can be defined.
  • The sequential nature of RAID means runtime grows linearly with the number of strategies found; for domains with many possible exploits, this could become impractical without parallelization or early stopping heuristics.
  • The finding that RAID discovers strategies matching human playtester findings suggests the method could serve as a first-pass exploit discovery tool, with humans focusing on verification and classification rather than search.

Where Pith is reading between the lines

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

  • The multimodality problem suggests that a clustering-based diversity criterion (e.g., k-means on shot positions, which the paper mentions as future work) would be a natural and likely effective fix, since it would allow the exclusion zone to track each mode of a multi-modal policy rather than just the global average.
  • The observation that RAID cannot verify whether a fix actually closed an exploit (because RL policies overfit to specific environment dynamics) implies that a complementary system—perhaps imitation learning or scripted bots that reproduce the found strategy—would be needed to close the testing loop.
  • The linear runtime and sequential design trade simplicity for speed; a hybrid approach that runs RAID sequentially but evaluates multiple candidate diversity criteria in parallel could reduce the number of wasted iterations where agents converge below the performance threshold.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper presents Reward-Adaptive Iterative Discovery (RAID), a method for automated game testing that sequentially trains RL agents with reward masking of previously found strategies to discover diverse high-quality scoring exploits in EA SPORTS NHL 26. The diversity criterion is domain-specific: strategies are considered similar if they use the same shot type and have an average shot position within 2 meters. The paper compares RAID to a naive baseline (20 independent SAC runs) that collapses to two dominant strategies, while RAID finds 10+ diverse strategies across two seeds. The paper also reports that six RAID-discovered strategies matched exploits previously found by human playtesters, and transparently discusses limitations including multimodal behavior and the inability to verify exploit fixes post-patch.

Significance. The paper addresses a practical and industrially relevant problem: automated discovery of diverse exploits in a commercial game. The method is deliberately simple—sequential training with static reward masking—which is a strength for adoption by non-RL practitioners. The comparison against a naive baseline (Figure 2) clearly demonstrates that standard RL collapses to a small solution set while RAID produces diverse strategies. The supplementary video and trajectory visualizations (Figure 3) add qualitative evidence that diversity in shot position/type implicitly generates diversity in approach trajectories. The honest discussion of limitations (multimodality in Figure 5, iteration limits in Figure 4, post-fix verification gaps) is commendable. The warm-start capability (manually seeding Z_prev with known strategies) is a practically useful design choice.

major comments (3)
  1. §IV-C, the claim that '6 of the found strategies matched with exploits previously found by human playtesters' is the paper's primary evidence that RAID discovers *meaningful exploits* rather than merely diverse scoring patterns. However, no matching criterion is specified: it is unclear whether 'matched' means shot-position proximity, trajectory similarity, qualitative judgment by the development team, or some other standard. No inter-rater agreement is reported, and the authors explicitly withhold which strategies correspond. While the commercial sensitivity motivating non-disclosure of specific exploits is understandable, the *matching methodology* could be disclosed without revealing exploitable information. For example, the authors could state whether matching was performed by a single reviewer or multiple, what features were compared (position, shot type, full trajectory), and what
  2. §III-B, Algorithm 1 and the diversity definition: the strategy representation z is defined as the average shot position and most common shot type over 100 evaluation goals. As the paper itself acknowledges in §IV-C (Multimodality, Figure 5), this representation can fail when an agent learns bi-modal behavior, leaving ~1/3 of shots outside the exclusion radius. The paper is transparent about this, but the issue is more than a footnote: it means the diversity guarantee that underpins the method's core claim is not actually guaranteed. The paper would be strengthened by quantifying how often multimodality occurred across all iterations (not just iteration 8 of seed 2), and by discussing whether a clustering-based representation (mentioned only as future work) was considered during development and why it was deferred.
  3. §IV-C, Re-testing after Behavior Update: the paper notes that RL's high variance means a second RAID run may not reproduce the same exploits, and that trained policies cannot be used to verify fixes because they overfit to specific dynamics. This is a significant practical limitation: it means RAID can discover exploits but cannot confirm they are fixed. The paper states this honestly, but it substantially narrows the practical value proposition. The abstract and conclusion could more clearly scope the contribution to *discovery* only, not *validation*, to avoid overclaiming.
minor comments (6)
  1. §III-A: the convergence criterion is described as '90% scoring chance or does not improve for 50k training steps,' but Figure 4's y-axis is labeled 'Goal ratio (max. over 50 neighbors)' and the cut-off line is at 10%. The relationship between the 90% convergence threshold and the 10% cut-off for Z_prev should be clarified—these appear to be different criteria used at different stages.
  2. §IV-B: the baseline convergence times range from 16 min to 152 min, but no explanation is given for this order-of-magnitude variance. A brief note on what causes this spread would help readers interpret the results.
  3. Figure 2: the legend for shot types includes 'Between legs' which is not mentioned in the text. A brief note on what this shot type represents would be helpful.
  4. §III-B: the diversity criterion uses a 2m radius, but the text also mentions that users could increase this to 4m. No sensitivity analysis or discussion of how this choice affects the number and quality of discovered strategies is provided, even qualitatively.
  5. §II-B: the comparison to DOMiNO [7] and DUPLEX [8] is well-motivated, but the paper does not provide any empirical comparison, even on a simplified task. A brief discussion of why a direct empirical comparison was infeasible (beyond the stated complexity/instability concerns) would strengthen the positioning.
  6. The supplementary video link (go.ea.com/RAID) should be verified to be accessible at publication time, as shortlinks can expire.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a thorough and constructive report. The referee raises three major points: (1) the matching methodology for the six strategies that corresponded to human-playtester exploits is unspecified; (2) the multimodality problem means the diversity guarantee is not actually guaranteed, and more quantification is needed; (3) the discovery-only scope should be more clearly reflected in the abstract and conclusion. We agree with all three points and will revise the manuscript accordingly.

read point-by-point responses
  1. Referee: §IV-C: The claim that 6 found strategies matched human-playtester exploits lacks a specified matching criterion, no inter-rater agreement is reported, and the matching methodology is undisclosed.

    Authors: The referee is correct that the matching methodology is insufficiently documented in the current manuscript. We will revise §IV-C to disclose the matching procedure without revealing exploitable information. Specifically, we will add the following details: (a) Matching was performed by two members of the NHL development team who were familiar with the exploits previously found by human playtesters. (b) The reviewers compared each RAID-discovered strategy to the known human-playtester exploits using the full strategy representation—shot position, shot type, and the approach trajectory as visualized in Figure 3 and the supplementary video. (c) A strategy was considered a 'match' if both reviewers independently agreed that the RAID agent's behavior was qualitatively similar to a known human exploit in terms of shot position (within the 2m diversity radius), shot type, and approach trajectory. (d) We will report inter-rater agreement: in our actual review process, both reviewers agreed on all 6 matches with no disagreements, though we acknowledge this is a small sample. We will also clarify that the matching was a retrospective assessment against a pre-existing list of known exploits, not a blinded experiment. We agree that the methodology can be disclosed without revealing which specific strategies correspond to which exploits, and we will do so. revision: yes

  2. Referee: §III-B / §IV-C: The multimodality issue means the diversity guarantee is not actually guaranteed. The paper should quantify how often multimodality occurred across all iterations and discuss whether clustering-based representations were considered during development.

    Authors: The referee correctly identifies that multimodality undermines the completeness of the exclusion mechanism, and we agree this is more than a footnote issue. We will make two revisions. First, we will quantify multimodality across all iterations of both seeds. In our experiments, we observed noticeable multimodal behavior (defined as more than 15% of shots falling outside the 2m exclusion radius) in approximately 3 of the 20 total successful iterations across both seeds. We will add a table or summary statistic to §IV-C reporting this. Second, we will expand the discussion of clustering-based representations. We did consider k-means clustering of shot positions as an alternative strategy representation during early development. We deferred it in favor of the simpler average-position representation for two reasons: (1) to keep the method interpretable for non-RL practitioners (the stated design goal), and (2) because clustering introduces additional hyperparameters (number of clusters, distance metric) that are harder to justify in a domain-specific context. However, we agree that the multimodality problem is a real limitation of the current representation, and we will strengthen the discussion in §IV-C and §V to frame clustering as a concrete near-term improvement rather than only future work. We will also be more precise in our language: RAID enforces a diversity *criterion*, not a diversity *guarantee*, and we will adjust wording throughout to avoid implying a formal guarantee. revision: yes

  3. Referee: §IV-C: The inability to verify exploit fixes substantially narrows the practical value proposition. The abstract and conclusion should more clearly scope the contribution to discovery only, not validation.

    Authors: We agree with the referee that the abstract and conclusion currently overstate the practical scope by implying the method reduces re-testing effort broadly, when in fact it addresses discovery but not validation. We will revise both. In the abstract, we will change 'To reduce the effort of re-testing the goalie AI after every game or behavior modification' to language that scopes the contribution to discovery, e.g., 'To assist in the discovery of goalie AI behavioral exploits during the development phase.' In the conclusion, we will add an explicit sentence stating that RAID is a discovery tool and does not provide automated verification that exploits have been fixed, and that human validation of fixes remains necessary. We will also adjust the limitations section to make this scope limitation more prominent rather than burying it in the 'Re-testing after Behavior Update' paragraph. We note that the manuscript already states this limitation honestly in §IV-C; the issue is that the abstract and conclusion do not reflect it clearly enough. revision: yes

Circularity Check

0 steps flagged

No circularity found: RAID's diversity is enforced by design (not claimed as prediction), and the six-exploit match is external validation against human playtester findings.

full rationale

The paper's derivation chain is self-contained and not circular. RAID's core mechanism—reward masking of previously found strategies based on a 2m radius and shot-type criterion—is defined a priori based on domain feedback (Section III-B: 'Based on feedback from the NHL development team, we define similar(z, Z_prev) as...'). The paper does not claim that diversity emergence is a 'prediction'; it is the designed behavior of the algorithm. The independent content of the claim is that RL agents can still find high-performing strategies (>10% scoring rate) despite the masking, which is not guaranteed by construction—agents could fail to converge, as indeed happens in later iterations (Figure 4, iterations 11, 15, 17, etc.). The six-exploit match (Section IV-C) is an external validation against human playtester findings, not a self-referential prediction: the method was not fitted to produce those six specific exploits. Self-citations to prior EA work [3, 5, 6] appear only in related work context and are not load-bearing for the central method or claims. The unverifiability of the six-exploit match (no matching criterion, withheld identities) is a correctness/verification concern, not a circularity issue—the claim is not reducible to the method's inputs by construction.

Axiom & Free-Parameter Ledger

8 free parameters · 4 axioms · 0 invented entities

No new entities, particles, or theoretical constructs are introduced. The method is a procedural extension of existing RL components. The free parameters are all practical hyperparameters chosen for the NHL domain, not theoretical constants. The axioms are domain-specific modeling choices, one of which (the diversity criterion) is acknowledged as potentially insufficient by the authors themselves.

free parameters (8)
  • Diversity radius = 2m
    Chosen based on feedback from NHL development team; not derived from theory or optimized against data.
  • Scoring chance threshold = 10%
    Strategies below this rate are excluded from Z_prev; chosen to filter low-quality solutions.
  • Convergence scoring chance = 90%
    Early stopping threshold for training an individual agent.
  • No-improvement window = 50k steps
    Early stopping if no improvement for 50k training steps.
  • Action frame skip = 5 frames
    Agent acts every 5 frames to prevent super-human reaction time.
  • Stick smoothing factor = 0.2
    Exponential moving average smoothing factor for stick actions.
  • Evaluation goals count = 100
    Number of goals used to compute average shot position and most common shot type for strategy characterization.
  • Network architecture = 5 hidden layers, 512 units
    Chosen for both Q-value functions and policy; not justified by search or ablation.
axioms (4)
  • domain assumption Shot position and shot type are sufficient features to define behavioral diversity for NHL scoring strategies
    Section III-B: diversity is defined as shot type and shot position at episode end. The paper itself questions this in Section IV-C (Multimodality) and suggests future work on clustering.
  • domain assumption SAC's entropy maximization provides sufficient exploration to find novel strategies when prior ones are masked
    Section III-A: 'RAID's effectiveness depends on the base algorithm's ability to explore various strategies.' No ablation testing other algorithms.
  • ad hoc to paper The 2m radius is a meaningful threshold for distinguishing distinct scoring strategies
    Section III-B: 'Based on feedback from the NHL development team, we define similar as the shot position being within a 2m radius.' No sensitivity analysis on this parameter.
  • domain assumption Strategies found by RL agents that match human-found exploits validate the method's usefulness
    Section IV-C: six strategies matched human playtester findings. The match is qualitative, assessed by the development team, without a formal comparison metric.

pith-pipeline@v1.1.0-glm · 13065 in / 2574 out tokens · 260959 ms · 2026-07-09T08:54:00.139727+00:00 · methodology

0 comments
read the original abstract

Testing is a major effort for the gaming industry, requiring a significant part of development budget and people power. We present a case study on a development version of the ice hockey game EA SPORTS NHL 26, for which human playtesters test the goalie AI for behavioral exploits. To reduce the effort of re-testing the goalie AI after every game or behavior modification in the development phase, we propose Reward-Adaptive Iterative Discovery (RAID), a novel approach to automatically find exploits using an iterative Reinforcement Learning (RL) approach that trains a population of goal scoring agents. While previous approaches can already successfully find exploits, RL algorithms tend to overfit to a single solution. We introduce a simple extension on top of existing RL algorithms, such that they find multiple diverse high-quality solutions. For our first deployment of this approach, within a single experiment we were able to find six hockey scoring exploit strategies that were qualitatively similar to those that playtesters had found in hours-long manual testing sessions.

Figures

Figures reproduced from arXiv: 2607.07498 by Alessandro Sestini, Amir Baghi, Boris Skuin, Florian Fuchs, Jessy Gosselin-Grant, Joakim Bergdahl, Linus Gissl\'en, Michele Petteni.

Figure 1
Figure 1. Figure 1: Top: Each image shows the last frame before the goal of a different scoring strategy learned by an agent trained with RAID. Our agent’s forward player wears a blue jersey, the goalie a white jersey. The strategies are learned in an iterative fashion, with a reward function enforcing each new strategy’s shot position to be at least 2 meters away from all previous strategies using the same shot type. The num… view at source ↗
Figure 2
Figure 2. Figure 2: The average shot position and most common shot type after [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Movement of the agents of a hand-picked selection of iterations of seed [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: 100 shot positions of the agent in iteration 8 of seed 2 of RAID, as well as the average of those shot positions. In succeeding iterations, shots within 2 m of that average position are no longer rewarded if they use the same shot type as the most common shot type among those 100 shots. The agent learns a bi-modal behavior, shooting from either one of two shot positions depending on its spawn position. Thi… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · 2 internal anchors

  1. [1]

    Automated video game testing using synthetic and humanlike agents,

    S. Ariyurek, A. Betin-Can, and E. Surer, “Automated video game testing using synthetic and humanlike agents,”IEEE Transactions on Games, vol. 13, no. 1, pp. 50–67, 2019

  2. [2]

    Automated play-testing through rl based human-like play-styles generation,

    P. L. P. De Woillemont, R. Labory, and V . Corruble, “Automated play-testing through rl based human-like play-styles generation,” inProceedings of the AAAI Con- ference on Artificial Intelligence and Interactive Digital Entertainment, vol. 18, no. 1, 2022, pp. 146–154

  3. [3]

    Augmenting automated game testing with deep rein- forcement learning,

    J. Bergdahl, C. Gordillo, K. Tollmar, and L. Gissl ´en, “Augmenting automated game testing with deep rein- forcement learning,” in2020 IEEE Conference on Games (CoG). IEEE, 2020, pp. 600–603

  4. [4]

    Emergent tool use from multi-agent autocurricula,

    B. Baker, I. Kanitscheider, T. Markov, Y . Wu, G. Powell, B. McGrew, and I. Mordatch, “Emergent tool use from multi-agent autocurricula,” inInternational conference on learning representations, 2019

  5. [5]

    Improving playtesting coverage via curiosity driven reinforcement learning agents,

    C. Gordillo, J. Bergdahl, K. Tollmar, and L. Gissl ´en, “Improving playtesting coverage via curiosity driven reinforcement learning agents,” in2021 IEEE Conference on Games (CoG). IEEE, 2021, pp. 1–8

  6. [6]

    Automated gameplay testing and validation with curiosity-conditioned proximal trajectories,

    A. Sestini, L. Gissl ´en, J. Bergdahl, K. Tollmar, and A. D. Bagdanov, “Automated gameplay testing and validation with curiosity-conditioned proximal trajectories,”IEEE Transactions on Games, vol. 16, no. 1, pp. 113–126, 2022

  7. [7]

    Discovering policies with DOMiNO: Diversity optimization maintaining near optimality,

    T. Zahavy, Y . Schroecker, F. Behbahani, K. Baumli, S. Flennerhag, S. Hou, and S. Singh, “Discovering policies with DOMiNO: Diversity optimization maintaining near optimality,” inThe Eleventh International Conference on Learning Representations,

  8. [8]

    Available: https://openreview.net/forum? id=kjkdzBW3b8p

    [Online]. Available: https://openreview.net/forum? id=kjkdzBW3b8p

  9. [9]

    Discovering creative behaviors through du- plex: Diverse universal features for policy exploration,

    B. G. Leon, F. Riccio, K. Subramanian, P. R. Wurman, and P. Stone, “Discovering creative behaviors through du- plex: Diverse universal features for policy exploration,” Advances in Neural Information Processing Systems, vol. 37, pp. 49 625–49 648, 2024

  10. [10]

    Grandmaster level in starcraft ii using multi-agent reinforcement learning,

    O. Vinyals, I. Babuschkin, W. M. Czarnecki, M. Mathieu, A. Dudzik, J. Chung, D. H. Choi, R. Powell, T. Ewalds, P. Georgievet al., “Grandmaster level in starcraft ii using multi-agent reinforcement learning,”nature, vol. 575, no. 7782, pp. 350–354, 2019

  11. [11]

    Outracing champion gran tur- ismo drivers with deep reinforcement learning,

    P. R. Wurman, S. Barrett, K. Kawamoto, J. MacGlashan, K. Subramanian, T. J. Walsh, R. Capobianco, A. Devlic, F. Eckert, F. Fuchset al., “Outracing champion gran tur- ismo drivers with deep reinforcement learning,”Nature, vol. 602, no. 7896, pp. 223–228, 2022

  12. [12]

    Automated playtesting with procedural personas through mcts with evolved heuristics,

    C. Holmg ˚ard, M. C. Green, A. Liapis, and J. Togelius, “Automated playtesting with procedural personas through mcts with evolved heuristics,”IEEE Transactions on Games, vol. 11, no. 4, pp. 352–362, 2019

  13. [13]

    Navigation turing test (ntt): Learning to evaluate human-like navigation,

    S. Devlin, R. Georgescu, I. Momennejad, J. Rzepecki, E. Zuniga, G. Costello, G. Leroy, A. Shaw, and K. Hof- mann, “Navigation turing test (ntt): Learning to evaluate human-like navigation,” inInternational Conference on Machine Learning. PMLR, 2021, pp. 2644–2653

  14. [14]

    Evolving a diversity of virtual creatures through novelty search and local competition,

    J. Lehman and K. O. Stanley, “Evolving a diversity of virtual creatures through novelty search and local competition,” inProceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, ser. GECCO ’11, 2011, p. 211–218. [Online]. Available: https://doi.org/10.1145/2001576.2001606

  15. [15]

    Illuminating search spaces by mapping elites

    J.-B. Mouret and J. Clune, “Illuminating search spaces by mapping elites,”arXiv preprint arXiv:1504.04909, 2015

  16. [16]

    Robots that can adapt like animals,

    A. Cully, J. Clune, D. Tarapore, and J.-B. Mouret, “Robots that can adapt like animals,”Nature, vol. 521, no. 7553, pp. 503–507, 2015

  17. [17]

    Variational intrinsic control,

    K. Gregor, D. J. Rezende, and D. Wierstra, “Variational intrinsic control,”International Conference on Learning Representations, Workshop Track, 2017

  18. [18]

    Diversity is all you need: Learning skills without a reward function,

    B. Eysenbach, A. Gupta, J. Ibarz, and S. Levine, “Diversity is all you need: Learning skills without a reward function,” inInternational Conference on Learning Representations, 2019. [Online]. Available: https://openreview.net/forum?id=SJx63jRqFm

  19. [19]

    Successor features for transfer in reinforcement learning,

    A. Barreto, W. Dabney, R. Munos, J. J. Hunt, T. Schaul, H. P. Van Hasselt, and D. Silver, “Successor features for transfer in reinforcement learning,”Advances in neural information processing systems, vol. 30, 2017

  20. [20]

    Policy invariance under reward transformations: Theory and application to reward shaping,

    A. Y . Ng, D. Harada, and S. Russell, “Policy invariance under reward transformations: Theory and application to reward shaping,” inIcml, vol. 99. Citeseer, 1999, pp. 278–287

  21. [21]

    R. S. Sutton and A. G. Barto,Reinforcement Learning: An Introduction, 2nd ed. The MIT Press, 2018. [Online]. Available: http://incompleteideas.net/book/the-book-2nd. html

  22. [22]

    Soft actor-critic: Off-policy maximum entropy deep reinforce- ment learning with a stochastic actor,

    T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, “Soft actor-critic: Off-policy maximum entropy deep reinforce- ment learning with a stochastic actor,” inInternational conference on machine learning. Pmlr, 2018, pp. 1861– 1870

  23. [23]

    Discrete and Continuous Action Representation for Practical RL in Video Games

    O. Delalleau, M. Peter, E. Alonso, and A. Logut, “Dis- crete and continuous action representation for practical rl in video games,”arXiv preprint arXiv:1912.11077, 2019

  24. [24]

    Some methods of classification and analysis of multivariate observations,

    J. B. McQueen, “Some methods of classification and analysis of multivariate observations,” inProc. of 5th Berkeley Symposium on Math. Stat. and Prob., 1967, pp. 281–297