---
title: Relative Human Action Efficiency (RHAE)
url: https://www.emergentmind.com/topics/relative-human-action-efficiency-rhae
type: topic
---

# Relative Human Action Efficiency (RHAE)

Searching arXiv for the cited papers to ground the article and confirm metadata.
Relative Human Action Efficiency (RHAE) is a family of human-referenced efficiency constructs used to compare an action sequence, controller, policy, or actuation system against a human baseline, a human-determined reference trajectory, or a human task-demand envelope. It is not introduced as a named metric in the cited literature, but multiple papers provide closely related formalizations. In program induction, the most direct formulation compares human flattened action length to an optimal flat solution length [1807.07134]. In computer-use benchmarking, the closest explicit human-relative factor is the ratio of expected human-performed number of steps to actual agent-generated number of steps, embedded in the Weighted Efficiency Score (WES) [2506.16042]. In human-robot interaction and actuation, related work generalizes the idea toward relative reductions in human effort, duration-sensitive coupling, joint human-robot coefficiency, relative action comparison, and human-equivalent actuation adequacy [2407.14161], [2210.11660], [2306.07205], [2605.01194], [2511.06796]. Across these settings, RHAE denotes not a single canonical scalar but a structured comparison between observed behavior and a human-relevant efficiency reference.

## 1. Conceptual scope and definitional variants

The clearest antecedent to RHAE appears in “Representational efficiency outweighs action efficiency in human program induction” [1807.07134], which distinguishes **action efficiency** from **representational efficiency**. In that work, action efficiency is minimizing the number of primitive actions executed, while representational efficiency is minimizing stored program size. The paper does not define a metric called “Relative Human Action Efficiency” explicitly, but it provides almost everything needed to construct one [1807.07134].

In that formulation, a hierarchical program \(P\) induces a flattened action sequence \(\mathrm{flat}(P)\), and action count is operationalized as
\[
A(P)=|\mathrm{flat}(P)|.
\]
The paper-grounded action baseline is the optimal flat solution, denoted in the supplied material as
\[
A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,
\]
approximated empirically by the best PPO rollout [1807.07134]. A directly supported RHAE-style ratio is therefore
\[
\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},
\]
with \(A_{\text{human}}=|\pi_{\text{human}}|\) for flat solutions and \(A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|\) for hierarchical solutions [1807.07134]. A complementary regret form is
\[
\mathrm{RHAE}_{\text{regret}}=A_{\text{human}}-A^*_{\text{flat}}.
\]

A second major variant appears in “OSWorld-Human: Benchmarking the Efficiency of Computer-Use Agents” [2506.16042]. There, the human-relative comparison is between the expected, human-performed number of steps \(t_{exp}\) and the actual, agent-generated number of steps \(t_{actual}\). The paper’s success-side efficiency factor is
\[
\frac{t_{exp}}{t_{actual}},
\]
which is the closest direct analog to RHAE in that benchmark [2506.16042]. The paper does not name this ratio RHAE, but it explicitly uses it inside \(\mathrm{WES}^+\).

These two formulations already show that RHAE is domain-dependent. In one case, the denominator is a human solution’s primitive action count and the numerator is an optimal action baseline [1807.07134]. In another, the numerator is a human-determined reference trajectory and the denominator is an agent trajectory [2506.16042]. This suggests that RHAE is best treated as a human-relative efficiency schema rather than a single standardized metric.

## 2. Action-count RHAE in program induction

The program-induction formulation is grounded in a Lightbot task cast under the Markov Decision Process framework [1807.07134]. Primitive actions are: walk, jump, turn right, turn left, and toggle light. States in the RL implementation contain the direction the robot is facing, the height of the current square, the coordinates of the robot, and a binary vector over lights, indicating which lights are on:
\[
s=(\text{orientation},\text{height},\text{position},\mathbf{l}),
\]
where \(\mathbf{l}\in\{0,1\}^m\) for \(m\) light tiles [1807.07134].

The core distinction is between flat solutions and hierarchical solutions. Flat solutions are sequences over primitive actions only. Hierarchical solutions are programs consisting of a main program, up to four stored sub-processes, calls to primitive actions or sub-processes, and possible self-calls, allowing simple recursion. The length of a program is defined as the number of instructions stored in the main program and sub-processes, while flattened program length is the full primitive action sequence generated by expanding subprocesses [1807.07134]. This yields the paired measures
\[
L(P)=|M|+\sum_{i=1}^4|S_i|
\qquad\text{and}\qquad
A(P)=|\mathrm{flat}(P)|.
\]

This setting is important for RHAE because it isolates a case in which action efficiency and representational efficiency diverge sharply. In flat conditions, participant solutions were close to optimal but significantly longer on average than the optimal flat solutions, yet the mode distance from optimal was 0 in both flat conditions; 61% of solutions in the Efficient Flat condition were optimal flat solutions and 55% of solutions in the Default Flat condition were optimal flat solutions [1807.07134]. This indicates that humans can often find action-minimizing or near-action-minimizing behavior when the representation is flat.

However, in hierarchy conditions, mean normalized flattened length in both hierarchy conditions was significantly greater than in both flat conditions, while the stored hierarchical programs themselves were significantly shorter than the flat solutions [1807.07134]. The supplied material summarizes the dissociation as lower \(L(P)\) but higher \(A(P)\) in hierarchy conditions. The clearest quantified example is puzzle 1: shortest flat solution length 46, best compression of that shortest flat solution 29, a much shorter hierarchical solution with stored length 22, but flattened action sequence 87 [1807.07134]. In the supplied interpretation, this yields action regret \(87-46=41\), action ratio \(46/87\approx 0.529\), and excess action proportion \((87-46)/46\approx 0.891\) [1807.07134].

The significance of this literature for RHAE is twofold. First, it provides an operational action baseline, \(A^*_{\text{flat}}\), that is explicit and puzzle-specific [1807.07134]. Second, it shows that low RHAE in hierarchical settings is not necessarily a failure; it may reflect deliberate bias toward representational compression. This directly addresses a likely misconception: human action inefficiency relative to a shortest-path baseline can coexist with structured, compressible, and cognitively preferred solutions [1807.07134].

## 3. Human-referenced step efficiency in computer-use agents

The most explicit human-relative efficiency benchmark in the supplied literature is “OSWorld-Human: Benchmarking the Efficiency of Computer-Use Agents” [2506.16042]. OSWorld-Human is a manually annotated version of the 369-task OSWorld benchmark, where each task is paired with a human-determined trajectory describing the steps needed to complete it [2506.16042]. OSWorld spans Ubuntu, Windows, and macOS and contains 369 real-world tasks over 9 applications [2506.16042].

The benchmark’s key premise is that accuracy alone is insufficient because agents may succeed on OSWorld yet still be unusably slow in practice. The paper emphasizes that state-of-the-art systems can take tens of minutes on tasks that humans would complete in a few minutes or less [2506.16042]. It therefore introduces a human-reference baseline intended to capture the “minimal humanly-perceived steps required to successfully complete a task” [2506.16042].

The paper’s formal aggregate metric is the Weighted Efficiency Score. For a task \(t\), let \(r_t=1\) if the task is successfully completed and \(r_t=0\) otherwise, with \(t_{exp}\) the expected number of steps from OSWorld-Human, \(t_{actual}\) the number of steps taken by the agent, and \(S\) the maximum number of steps allowed for that agent/system. The supplied material gives
\[
\mathrm{WES}^+=\sum_t^n r_t\left(\frac{t_{exp}}{t_{actual}}\right)
\]
and
\[
\mathrm{WES}^-=\sum_t^n -(1-r_t)\left(\frac{t_{actual}}{S}\right)
\]
[2506.16042]. The success-side term is the most direct RHAE-like quantity:
\[
\mathrm{RHAE}(t)=\frac{t_{exp}}{t_{actual}}.
\]

A useful counterpart is the inefficiency ratio
\[
\rho(t)=\frac{t_{actual}}{t_{exp}},
\]
with \(\rho=1\) indicating human-level step efficiency and \(\rho>1\) indicating that the agent uses more actions than the human reference [2506.16042]. The paper reports that even the highest-scoring agents on OSWorld take 1.4–2.7x more steps than necessary [2506.16042].

OSWorld-Human contains two reference variants: a **single-action trajectory**, where every necessary action is counted individually, and a **grouped-action trajectory**, where multiple consecutive actions are grouped into one step if they can be executed from the same visual observation without requiring another observation/prediction cycle [2506.16042]. This distinction is methodologically important. A single-action RHAE measures primitive-action efficiency relative to a human primitive-action baseline, whereas a grouped-action RHAE measures decision/observation-cycle efficiency relative to what a human could plausibly batch into one observation-planning unit. This suggests that RHAE may need multiple granularities when interaction latency is dominated by repeated planning and observation loops.

The empirical results make the separation between success and efficiency especially clear. For example, Agent S2 w/ Gemini 2.5 has Original OSWorld score 41.4%, Single-action \(\mathrm{WES}^+\) 28.2%, and Grouped-action \(\mathrm{WES}^+\) 17.4% [2506.16042]. The supplied interpretation states that this corresponds to a 1.5x reduction from 41.4 to 28.2 and a 2.4x reduction from 41.4 to 17.4, and that “Intuitively, this represents the average number of extra steps the agent takes” [2506.16042]. More generally, the paper’s summary range 1.4–2.7x longer trajectories than necessary furnishes a concrete human-relative inefficiency interval for state-of-the-art computer-use agents [2506.16042].

## 4. Multidimensional RHAE in human-robot collaboration

In physical human-robot interaction, efficiency is not reducible to action count. “Efficient and Safe Contact-rich pHRI via Subtask Detection and Motion Estimation using Deep Learning” explicitly aims to minimize human effort and task completion time while maximizing precision and stability during contact with the workpiece [2407.14161]. The task is decomposed into four subtasks: Idle, Tool-Attachment, Driving, and Contact [2407.14161]. The efficiency objective is subtask-specific: Driving efficiency corresponds to low resistance, low human force, low total effort, and high average velocity, while Contact efficiency is dominated by low oscillation, stable interaction, and safe contact onset [2407.14161].

The paper defines average human force during Driving as
\[
F_h^{\mathrm{ave}}=\frac{1}{T_d}\int_{t_d}^{t_c}\|\mathbf{F}_h(t)\|\,dt,
\]
average velocity as
\[
V_{\mathrm{ave}}=\frac{1}{T_d}\int_{t_d}^{t_c}\|\mathbf{V}(t)\|\,dt,
\]
and total human effort as
\[
E_h^{\mathrm{tot}}=\int_{t_d}^{t_c}\|\mathbf{F}_h(t)\|\,\|\mathbf{V}(t)\|\,dt
\]
[2407.14161]. The principal contact-stability metric is oscillation amplitude at Contact, expressed as the maximum magnitude observed in the spectrogram of detrended end-effector velocity [2407.14161]. The paper reports subtask classification accuracy of 84.46% online in virtual environments, weighted \(F_1\) of 0.8423, motion estimation \(R^2\) of 0.9562, 57% lower human effort during Driving, and 53% lower oscillation amplitude at Contact [2407.14161]. The supplied material notes that the 53% value is explicitly relative to the subtask detector alone, while the 57% effort reduction should be treated cautiously because the exact baseline condition is not explicitly specified in the summary [2407.14161].

This literature supports a multidimensional RHAE interpretation rather than a single scalar action-count ratio. The supplied derived forms include
\[
\mathrm{RHAE}_{E}(A\mid B)=1-\frac{E_{h,A}^{\mathrm{tot}}}{E_{h,B}^{\mathrm{tot}}}
\]
for effort,
\[
\mathrm{RHAE}_{O}(A\mid B)=1-\frac{O_A}{O_B}
\]
for contact stability, and a composite weighted form over effort, speed, and oscillation [2407.14161]. These expressions are derived interpretations rather than explicit definitions from the paper, but they are faithful to its measured variables.

A related but distinct perspective is given by “Learning Action Duration and Synergy in Task Planning for Human-Robot Collaboration” [2210.11660]. There, action efficiency is represented by expected duration, and collaborative efficiency is modulated by directional synergy coefficients. Baseline task durations are \(\hat d_i^H\) and \(\hat d_i^R\); human-side and robot-side synergy coefficients are \(s^H_{i,j}\) and \(s^R_{i,j}\); overlap fractions are \(\delta^H_{i,j}\) and \(\delta^R_{i,j}\) [2210.11660]. The plan objective is makespan,
\[
J=\max\{d_\pi^H,d_\pi^R\},
\]
with
\[
d_\pi^H=\sum_i \hat d_i^H a_i^H\left(\sum_j s^H_{i,j}\delta^H_{i,j}a_j^R\right)
\]
and
\[
d_\pi^R=\sum_i \hat d_i^R a_i^R\left(\sum_j s^R_{i,j}\delta^R_{i,j}a_j^H\right)
\]
[2210.11660]. A natural RHAE extrapolation from these definitions is
\[
\mathrm{RHAE}^{\text{collab}}_{i\mid j}=\frac{\hat d_i^H}{d_{i,j}^H}=\frac{1}{s^H_{i,j}},
\]
which interprets collaboration-induced duration inflation as a reduction in relative human efficiency [2210.11660]. This suggests that in collaborative planning, RHAE can be understood as inverse synergy-adjusted duration relative to a baseline expected human duration.

## 5. Dyadic and relative-action extensions

The most direct group-level generalization beyond human-only efficiency appears in “Maximising Coefficiency of Human-Robot Handovers through Reinforcement Learning” [2306.07205]. That paper imports the idea that “humans act coefficiently as a group,” glossed as “simultaneously maximising the benefits of all agents involved,” and formalizes a human-robot coefficiency score rather than a human-only efficiency ratio [2306.07205]. Human cognitive ergonomics is
\[
C_{\text{cognitive erg}}^{H}(a)=\frac{1}{2}\Big[(1-\tau)+\mathbb{E}_{t=t_0,\dots,t_f}[\Lambda(t)]\Big],
\]
human physical ergonomics is
\[
C_{\text{physical erg}}^{H}=\min_{t=t_0,\dots,t_f}\bar\zeta(t),
\]
robot energy efficiency is
\[
C_{\text{energy cons}}^{R}(a)=1-\frac{1}{E_{\max}}\int_{t_0}^{t_f}P(t)\,dt,
\]
and the joint score is
\[
C_{\text{coefficiency}}^{HR}(a)=\frac{1}{3}\Big[C_{\text{cognitive erg}}^{H}+C_{\text{physical erg}}^{H}+C_{\text{energy cons}}^{R}\Big]
\]
[2306.07205]. The reward used for reinforcement learning is exactly this coefficiency score.

This is not a strict RHAE definition because it lacks an explicit relative ratio such as human benefit per unit robot sacrifice [2306.07205]. Nonetheless, it is directly relevant because it rejects purely altruistic optimization and treats efficiency as a property of the dyad rather than the individual. A plausible implication is that some applications require a joint-action extension of RHAE rather than a human-only measure.

A different extension appears in “VLA-ATTC: Adaptive Test-Time Compute for VLA Models with Relative Action Critic Model” [2605.01194]. That paper is not about human-relative efficiency, but it provides a general relative-action evaluation mechanism. At each timestep, the system samples two action chunks, computes uncertainty by Dynamic Time Warping, and switches from fast execution to deliberation if uncertainty exceeds a threshold [2605.01194]. The uncertainty score is
\[
U_t=\mathcal{T}(H,H),
\]
where \(\mathcal{T}\) is the DTW cumulative cost matrix over candidate action chunks [2605.01194]. In deliberative mode, a Relative Action Critic outputs
\[
p_{ij}=R(a_i,a_j,C_t,s_t),
\]
the preference probability that action \(a_i\) is preferable to action \(a_j\), and a tournament selects the final action [2605.01194].

This relative evaluation framework is useful for RHAE because it suggests that contextual pairwise comparison may be more robust than absolute action scoring. The paper does not define a human-referenced metric, but it demonstrates that pairwise relative action evaluation can substantially improve long-horizon embodied performance, with PI0.5 success improving from 90.6% to 95.4% in the full setting, corresponding to over 50% failure-rate reduction, and adaptive deliberation retaining 20.8 Hz versus 23.3 Hz for baseline PI0/PI0.5 [2605.01194]. This suggests that future RHAE designs could compare candidate actions relatively and invoke costly evaluation selectively under uncertainty.

## 6. Human-relative actuation adequacy and limits of the term “efficiency”

“Human-Level Actuation for Humanoids” provides a rigorous human-relative comparison framework, but it is more directly about actuation adequacy than about action efficiency in a narrow sense [2511.06796]. Its central constructs are the DoF atlas, Human-Equivalence Envelopes (HEE), and the Human-Level Actuation Score (HLAS) [2511.06796].

For each joint-task pair \((j,t)\), HEE evaluates whether a robot meets human torque and power simultaneously at the same joint angle and rate \((q,\omega)\), weighted by positive mechanical work in task-specific bands [2511.06796]. The exact HEE definition is
\[
h^{(w)}_{j,t}=
\frac{\displaystyle \iint_{\mathcal{R}_{j,t}}
\mathbb{1}\!\left[T^{\mathrm{rob}}_j(q,\omega)\ge T^{\mathrm{hum}}_{j,t}(q,\omega)\land
P^{\mathrm{rob}}_j(q,\omega)\ge P^{\mathrm{hum}}_{j,t}(q,\omega)\right]
P^{\mathrm{hum}+}_{j,t}(q,\omega)\,dq\,d\omega}
{\displaystyle \iint_{\mathcal{R}_{j,t}}P^{\mathrm{hum}+}_{j,t}(q,\omega)\,dq\,d\omega}
\in[0,1]
\]
[2511.06796]. HLAS then aggregates ROM coverage, DoF sufficiency, HEE coverage, torque-mode bandwidth, task-weighted efficiency, and thermal sustainability:
\[
\mathrm{HLAS}
=
\sum_{t\in\mathcal{T}}w_t\sum_{j\in\mathcal{J}_t}u_{j,t}
\left[
\alpha_{\mathrm{ROM}}\rho^{\mathrm{ROM}}_{j,t}
+\alpha_{\mathrm{DoF}}d^{\mathrm{DoF}}_{j,t}
+\alpha_{\mathrm{HEE}}h^{(w)}_{j,t}
+\alpha_{\mathrm{bw}}b^\tau_{j,t}
+\alpha_{\eta}\eta_{j,t}
+\alpha_{\mathrm{therm}}\theta^{\mathrm{therm}}_{j,t}
\right]
\]
[2511.06796].

The task-weighted efficiency term itself is electromechanical:
\[
\eta_j(q,\omega)=\frac{P_{\mathrm{mech}}(q,\omega)}{P_{\mathrm{elec}}(q,\omega)},
\qquad
\bar\eta_{j,t}=
\frac{\sum_{(q,\omega)\in\mathcal{R}_{j,t}}\eta_j(q,\omega)P^{\mathrm{hum}+}_{j,t}(q,\omega)}
{\sum_{(q,\omega)\in\mathcal{R}_{j,t}}P^{\mathrm{hum}+}_{j,t}(q,\omega)}
\]
[2511.06796]. The worked example yields \(\mathrm{HLAS}=0.636\), with HEE identified as the main source of variation [2511.06796].

This literature clarifies an important conceptual boundary. A binary or weighted human-equivalence coverage such as HEE is not, strictly speaking, an efficiency metric; it is a relative capability coverage metric [2511.06796]. HLAS is a broader human-relative actuation adequacy score, not a pure RHAE [2511.06796]. A plausible implication is that some uses of the phrase “Relative Human Action Efficiency” conflate efficiency with adequacy, human-likeness, or actuation sufficiency. The cited framework argues against that conflation by separating torque-power coverage, efficiency, bandwidth, and thermal sustainability.

## 7. Synthesis, interpretation, and recurring caveats

Across the cited literature, RHAE can be organized into three recurrent forms. The first is **baseline-relative action economy**, exemplified by
\[
\frac{A^*_{\text{flat}}}{A_{\text{human}}}
\]
in program induction [1807.07134]. The second is **human-reference trajectory efficiency**, exemplified by
\[
\frac{t_{exp}}{t_{actual}}
\]
inside \(\mathrm{WES}^+\) on OSWorld-Human [2506.16042]. The third is **multidimensional human-relative execution efficiency**, where human effort, duration, stability, coupling, energy, or actuation adequacy are compared across conditions or against human demands [2407.14161], [2210.11660], [2306.07205], [2511.06796].

Several caveats recur. In OSWorld-Human, the trajectories are manually curated, consensus, task-validating reference trajectories rather than raw demonstrations from a diverse pool of humans [2506.16042]. In program induction, a low action-efficiency ratio can reflect deliberate optimization of representational efficiency rather than poor problem solving [1807.07134]. In contact-rich pHRI, no single scalar “efficiency” formula is defined; the most defensible interpretation is multicomponent and subtask-aware [2407.14161]. In synergy-based collaborative planning, estimated efficiency is contextual, directional, and overlap-dependent rather than intrinsic to an isolated task [2210.11660]. In handovers, coefficiency uses normalized additive aggregation rather than a true relative ratio [2306.07205]. In humanoid actuation, human-relative adequacy and energetic efficiency are separable constructs, and peak specifications are explicitly rejected as sufficient evidence of human-level action [2511.06796].

A common misconception is that RHAE must always denote fewer actions than a human or fewer steps than optimal. The cited work does not support such a universal interpretation. In some domains, human behavior is near action-optimal under flat representations but departs from the shortest-path baseline under hierarchical abstraction because representational compression is preferred [1807.07134]. In other domains, the relevant baseline is a human-determined minimal trajectory, and excess actions primarily matter because they amplify latency [2506.16042]. In still other domains, the relevant inefficiency lies in added human force, increased duration under concurrency, degraded contact stability, or insufficient torque-power coverage over task-relevant states [2407.14161], [2210.11660], [2511.06796].

The literature therefore supports a disciplined use of the term. RHAE is best understood as a human-referenced efficiency relation whose precise definition depends on what counts as the relevant human baseline: an optimal human-like flat solution, a human-determined task trajectory, a baseline expected human duration, a joint human-robot utility, or a human biomechanical demand envelope. Where a single scalar is needed, the most paper-faithful simple forms are \(\frac{A^*_{\text{flat}}}{A_{\text{human}}}\) for program-induction action counts [1807.07134] and \(\frac{t_{exp}}{t_{actual}}\) for human-referenced computer-use steps [2506.16042]. Where the task requires richer analysis, the literature indicates that RHAE should be decomposed into task-specific components rather than collapsed into an unqualified global score [2407.14161], [2210.11660], [2306.07205], [2511.06796].

Source: https://www.emergentmind.com/topics/relative-human-action-efficiency-rhae