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arxiv: 2604.24558 · v1 · submitted 2026-04-27 · 💻 cs.AI · cs.LG

Recognition: unknown

Hierarchical Behaviour Spaces

Michael Tryfan Matthews , Anssi Kanervisto , Jakob Foerster , Pierluca D'Oro , Scott Fujimoto , Mikael Henaff
Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:28 UTC · model grok-4.3

classification 💻 cs.AI cs.LG
keywords hierarchical reinforcement learningbehavior spaceslinear combinationsNetHackexplorationoptionspolicy expressiveness
0
0 comments X

The pith

Linear combinations of reward functions let a high-level controller create a continuous space of behaviors for low-level policies.

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

The paper shows that predefined reward functions need not each define one rigid option. Instead, the high-level controller can output weights that combine those rewards linearly, producing a richer family of target behaviors that low-level policies can pursue. This Hierarchical Behaviour Spaces method is tested in the NetHack Learning Environment and achieves strong results. Ablation studies indicate that the hierarchy helps mainly by improving exploration during training, not by enabling deeper long-term planning. A reader would care because the approach offers a practical way to expand policy expressiveness without hand-designing many separate options.

Core claim

We show that, instead of using a single reward function per option, the reward functions can be effectively used to induce a space of behaviours, by letting the controller specify linear combinations over reward functions, allowing a more expressive set of policies to be represented. We call this method Hierarchical Behaviour Spaces (HBS). We evaluate HBS on the NetHack Learning Environment, demonstrating strong performance. We conduct a series of experiments and determine that, perhaps going against conventional wisdom, the benefits of hierarchy in our method come from increased exploration rather than long term reasoning.

What carries the argument

Hierarchical Behaviour Spaces, the mechanism in which the controller outputs linear combinations over a fixed set of reward functions to define target behaviors for low-level policies.

If this is right

  • A small number of reward functions can generate a continuous range of policies rather than a discrete set of options.
  • Hierarchy improves learning primarily through broader exploration in complex environments.
  • Performance gains appear in NetHack because the expanded behavior space aids discovery of effective strategies.
  • Agents can represent more varied behaviors without additional reward engineering for each new option.

Where Pith is reading between the lines

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

  • The method may lower the cost of designing hierarchical agents by reducing the number of manually specified options needed.
  • Similar linear-combination spaces could be tested in other sparse-reward domains to check whether exploration benefits hold.
  • Combining the fixed reward basis with a learned component might allow the behavior space to adapt during training.

Load-bearing premise

Linear combinations of the predefined reward functions are expressive enough to cover useful behaviors and yield stable policies without extra safeguards against degenerate cases.

What would settle it

An experiment in which exploration is controlled or removed as a factor (for example by providing dense shaping rewards) and HBS shows no advantage over a non-hierarchical baseline.

Figures

Figures reproduced from arXiv: 2604.24558 by Anssi Kanervisto, Jakob Foerster, Michael Tryfan Matthews, Mikael Henaff, Pierluca D'Oro, Scott Fujimoto.

Figure 1
Figure 1. Figure 1: The n reward functions induce a n − 1 simplex of behaviours. The controller πΩ selects a linear combination of reward functions from the simplex, which the intra-option policy πω then acts to maximise for some number of timesteps. In this way, a large diversity of behaviours can be extracted from only a few reward functions. progress on the benchmark, reaching various parts of the game with a consistency h… view at source ↗
Figure 2
Figure 2. Figure 2: Results on the NetHack Learning Environment. The shaded areas denote 1 standard error view at source ↗
Figure 3
Figure 3. Figure 3: Visitation rates of early waypoints in NetHack for each method. The arrows indicate the view at source ↗
Figure 4
Figure 4. Figure 4: Results on the NetHack Learning Environment for PPO and HBS trained for 8 billion view at source ↗
Figure 5
Figure 5. Figure 5: Performance on the NLE as the option space grows for both SOL and HBS at 40 billion view at source ↗
read the original abstract

Recent work in hierarchical reinforcement learning has shown success in scaling to billions of timesteps when learning over a set of predefined option reward functions. We show that, instead of using a single reward function per option, the reward functions can be effectively used to induce a space of behaviours, by letting the controller specify linear combinations over reward functions, allowing a more expressive set of policies to be represented. We call this method Hierarchical Behaviour Spaces (HBS). We evaluate HBS on the NetHack Learning Environment, demonstrating strong performance. We conduct a series of experiments and determine that, perhaps going against conventional wisdom, the benefits of hierarchy in our method come from increased exploration rather than long term reasoning.

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 / 1 minor

Summary. The paper introduces Hierarchical Behaviour Spaces (HBS), a hierarchical reinforcement learning approach that uses linear combinations of predefined reward functions to induce a space of behaviors. This allows the controller to represent a more expressive set of policies compared to using a single reward function per option. The method is evaluated on the NetHack Learning Environment, where it achieves strong performance. A series of experiments leads the authors to conclude that the benefits of hierarchy in HBS arise primarily from increased exploration rather than from improved long-term reasoning or credit assignment.

Significance. If the results hold, this work is significant because it provides evidence against the conventional wisdom that hierarchical methods primarily help with long-term credit assignment. By showing that the main benefit is enhanced exploration through a behavior space induced by linear reward combinations, it opens new avenues for designing hierarchical RL systems that prioritize behavior diversity. The simplicity of the linear combination approach could make it widely applicable in environments where multiple reward functions are available, potentially improving scalability in complex domains like NetHack.

major comments (2)
  1. [Abstract] The central empirical claims—that HBS shows strong performance and that hierarchy benefits stem from exploration—are stated without any supporting data, metrics, baselines, or analysis. This is load-bearing for the paper's contribution, as the abstract supplies no implementation details, statistical results, ablation controls, or error analysis.
  2. [Experiments] To substantiate the claim that benefits come from increased exploration rather than long-term reasoning, specific experiments isolating these factors are required. For instance, comparisons to non-hierarchical agents with equivalent exploration mechanisms or ablations removing the linear combination aspect would be necessary to support the conclusion.
minor comments (1)
  1. The notation for linear combinations over reward functions should be formalized with equations in the method section for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments. We address each major comment below and will revise the manuscript to strengthen the abstract and experimental analysis.

read point-by-point responses

  1. Referee: [Abstract] The central empirical claims—that HBS shows strong performance and that hierarchy benefits stem from exploration—are stated without any supporting data, metrics, baselines, or analysis. This is load-bearing for the paper's contribution, as the abstract supplies no implementation details, statistical results, ablation controls, or error analysis.

    Authors: We agree that the abstract would benefit from including concrete quantitative support for the central claims. In the revised version, we will expand the abstract to incorporate key performance metrics from the NetHack experiments (e.g., scores or success rates relative to baselines) and a concise reference to the experimental findings on exploration versus long-term reasoning. This will provide immediate evidence while preserving the abstract's summary nature. revision: yes

  2. Referee: [Experiments] To substantiate the claim that benefits come from increased exploration rather than long-term reasoning, specific experiments isolating these factors are required. For instance, comparisons to non-hierarchical agents with equivalent exploration mechanisms or ablations removing the linear combination aspect would be necessary to support the conclusion.

    Authors: The manuscript reports a series of experiments that support the conclusion regarding exploration benefits. To more directly isolate the contributions of hierarchy and the linear reward combinations, we will add the suggested experiments in revision: comparisons against non-hierarchical agents equipped with matched exploration mechanisms, and ablations that disable the linear combination mechanism to quantify its effect on behavior diversity and performance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical method with independent evaluation

full rationale

The paper introduces Hierarchical Behaviour Spaces (HBS) as an empirical extension to hierarchical RL: predefined option reward functions are combined linearly by a controller to induce a behavior space, with performance evaluated on NetHack. The central claims (more expressive policies, benefits primarily from exploration) rest on experimental results rather than any derivation, equation, or fitted parameter that reduces to its own inputs by construction. No self-definitional steps, fitted-input predictions, load-bearing self-citations, uniqueness theorems, or ansatz smuggling appear in the provided abstract or high-level description. The work is self-contained against external benchmarks via direct environment evaluation, consistent with a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the method appears to rest on standard hierarchical RL assumptions about options and reward functions without introducing new postulated objects.

pith-pipeline@v0.9.0 · 5417 in / 1155 out tokens · 75870 ms · 2026-05-08T03:28:51.765996+00:00 · methodology

discussion (0)

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