Relative Human Action Efficiency (RHAE)

• Relative Human Action Efficiency (RHAE) is a human-referenced framework that quantifies efficiency by comparing agent actions or trajectories against human baselines in diverse domains such as program induction and human–robot interaction.
• It employs ratios—such as the optimal flat solution length over human action count and expected versus actual steps—to benchmark performance in areas including OSWorld-Human and efficient task planning.
• RHAE extends to multidimensional measures by incorporating factors like human effort, task duration, stability, and actuation adequacy for comprehensive, task-specific evaluations.

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 (Sanborn et al., 2018). 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) (Abhyankar et al., 19 Jun 2025). 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 (Niaz et al., 2024, Sandrini et al., 2022, Lagomarsino et al., 2023, Li et al., 2 May 2026, Sunbeam, 10 Nov 2025). 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” (Sanborn et al., 2018), 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 (Sanborn et al., 2018).

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 (Sanborn et al., 2018). 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 (Sanborn et al., 2018). 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” (Abhyankar et al., 19 Jun 2025). 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

$\mathrm{flat}(P)$0

which is the closest direct analog to RHAE in that benchmark (Abhyankar et al., 19 Jun 2025). The paper does not name this ratio RHAE, but it explicitly uses it inside $\mathrm{flat}(P)$1.

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 (Sanborn et al., 2018). In another, the numerator is a human-determined reference trajectory and the denominator is an agent trajectory (Abhyankar et al., 19 Jun 2025). 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 (Sanborn et al., 2018). 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: $\mathrm{flat}(P)$2 where $\mathrm{flat}(P)$3 for $\mathrm{flat}(P)$4 light tiles (Sanborn et al., 2018).

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 (Sanborn et al., 2018). This yields the paired measures

$\mathrm{flat}(P)$5

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 (Sanborn et al., 2018). 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 (Sanborn et al., 2018). The supplied material summarizes the dissociation as lower $\mathrm{flat}(P)$6 but higher $\mathrm{flat}(P)$7 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 (Sanborn et al., 2018). In the supplied interpretation, this yields action regret $\mathrm{flat}(P)$8, action ratio $\mathrm{flat}(P)$9, and excess action proportion $A(P)=|\mathrm{flat}(P)|.$0 (Sanborn et al., 2018).

The significance of this literature for RHAE is twofold. First, it provides an operational action baseline, $A(P)=|\mathrm{flat}(P)|.$1, that is explicit and puzzle-specific (Sanborn et al., 2018). 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 (Sanborn et al., 2018).

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” (Abhyankar et al., 19 Jun 2025). 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 (Abhyankar et al., 19 Jun 2025). OSWorld spans Ubuntu, Windows, and macOS and contains 369 real-world tasks over 9 applications (Abhyankar et al., 19 Jun 2025).

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 (Abhyankar et al., 19 Jun 2025). It therefore introduces a human-reference baseline intended to capture the “minimal humanly-perceived steps required to successfully complete a task” (Abhyankar et al., 19 Jun 2025).

The paper’s formal aggregate metric is the Weighted Efficiency Score. For a task $A(P)=|\mathrm{flat}(P)|.$2, let $A(P)=|\mathrm{flat}(P)|.$3 if the task is successfully completed and $A(P)=|\mathrm{flat}(P)|.$4 otherwise, with $A(P)=|\mathrm{flat}(P)|.$5 the expected number of steps from OSWorld-Human, $A(P)=|\mathrm{flat}(P)|.$6 the number of steps taken by the agent, and $A(P)=|\mathrm{flat}(P)|.$7 the maximum number of steps allowed for that agent/system. The supplied material gives

$A(P)=|\mathrm{flat}(P)|.$8

and

$A(P)=|\mathrm{flat}(P)|.$9

(Abhyankar et al., 19 Jun 2025). The success-side term is the most direct RHAE-like quantity: $$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$0

A useful counterpart is the inefficiency ratio

$$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$1

with $$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$2 indicating human-level step efficiency and $$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$3 indicating that the agent uses more actions than the human reference (Abhyankar et al., 19 Jun 2025). The paper reports that even the highest-scoring agents on OSWorld take 1.4–2.7x more steps than necessary (Abhyankar et al., 19 Jun 2025).

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 (Abhyankar et al., 19 Jun 2025). 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 $$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$4 28.2%, and Grouped-action $$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$5 17.4% (Abhyankar et al., 19 Jun 2025). 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” (Abhyankar et al., 19 Jun 2025). 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 (Abhyankar et al., 19 Jun 2025).

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 (Niaz et al., 2024). The task is decomposed into four subtasks: Idle, Tool-Attachment, Driving, and Contact (Niaz et al., 2024). 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 (Niaz et al., 2024).

The paper defines average human force during Driving as

$$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$6

average velocity as

$$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$7

and total human effort as

$$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$8

(Niaz et al., 2024). The principal contact-stability metric is oscillation amplitude at Contact, expressed as the maximum magnitude observed in the spectrogram of detrended end-effector velocity (Niaz et al., 2024). The paper reports subtask classification accuracy of 84.46% online in virtual environments, weighted $$A^*_{\text{flat}}=\min_{\pi\in\Pi_{\text{flat, valid}}}|\pi|,$$9 of 0.8423, motion estimation $$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$0 of 0.9562, 57% lower human effort during Driving, and 53% lower oscillation amplitude at Contact (Niaz et al., 2024). 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 (Niaz et al., 2024).

This literature supports a multidimensional RHAE interpretation rather than a single scalar action-count ratio. The supplied derived forms include

$$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$1

for effort,

$$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$2

for contact stability, and a composite weighted form over effort, speed, and oscillation (Niaz et al., 2024). 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” (Sandrini et al., 2022). There, action efficiency is represented by expected duration, and collaborative efficiency is modulated by directional synergy coefficients. Baseline task durations are $$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$3 and $$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$4; human-side and robot-side synergy coefficients are $$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$5 and $$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$6; overlap fractions are $$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$7 and $$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$8 (Sandrini et al., 2022). The plan objective is makespan,

$$\mathrm{RHAE}=\frac{A^*_{\text{flat}}}{A_{\text{human}}},$$9

with

$A_{\text{human}}=|\pi_{\text{human}}|$0

and

$A_{\text{human}}=|\pi_{\text{human}}|$1

(Sandrini et al., 2022). A natural RHAE extrapolation from these definitions is

$A_{\text{human}}=|\pi_{\text{human}}|$2

which interprets collaboration-induced duration inflation as a reduction in relative human efficiency (Sandrini et al., 2022). 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” (Lagomarsino et al., 2023). 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 (Lagomarsino et al., 2023). Human cognitive ergonomics is

$A_{\text{human}}=|\pi_{\text{human}}|$3

human physical ergonomics is

$A_{\text{human}}=|\pi_{\text{human}}|$4

robot energy efficiency is

$A_{\text{human}}=|\pi_{\text{human}}|$5

and the joint score is

$A_{\text{human}}=|\pi_{\text{human}}|$6

(Lagomarsino et al., 2023). 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 (Lagomarsino et al., 2023). 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” (Li et al., 2 May 2026). 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 (Li et al., 2 May 2026). The uncertainty score is

$A_{\text{human}}=|\pi_{\text{human}}|$7

where $A_{\text{human}}=|\pi_{\text{human}}|$8 is the DTW cumulative cost matrix over candidate action chunks (Li et al., 2 May 2026). In deliberative mode, a Relative Action Critic outputs

$A_{\text{human}}=|\pi_{\text{human}}|$9

the preference probability that action $A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$0 is preferable to action $A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$1, and a tournament selects the final action (Li et al., 2 May 2026).

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 (Li et al., 2 May 2026). 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 (Sunbeam, 10 Nov 2025). Its central constructs are the DoF atlas, Human-Equivalence Envelopes (HEE), and the Human-Level Actuation Score (HLAS) (Sunbeam, 10 Nov 2025).

For each joint-task pair $A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$2, HEE evaluates whether a robot meets human torque and power simultaneously at the same joint angle and rate $A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$3, weighted by positive mechanical work in task-specific bands (Sunbeam, 10 Nov 2025). The exact HEE definition is

$A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$4

(Sunbeam, 10 Nov 2025). HLAS then aggregates ROM coverage, DoF sufficiency, HEE coverage, torque-mode bandwidth, task-weighted efficiency, and thermal sustainability: $A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$5 (Sunbeam, 10 Nov 2025).

The task-weighted efficiency term itself is electromechanical: $A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$6 (Sunbeam, 10 Nov 2025). The worked example yields $A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$7, with HEE identified as the main source of variation (Sunbeam, 10 Nov 2025).

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 (Sunbeam, 10 Nov 2025). HLAS is a broader human-relative actuation adequacy score, not a pure RHAE (Sunbeam, 10 Nov 2025). 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

$A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$8

in program induction (Sanborn et al., 2018). The second is human-reference trajectory efficiency, exemplified by

$A_{\text{human}}=|\mathrm{flat}(P_{\text{human}})|$9

inside $$\mathrm{RHAE}_{\text{regret}}=A_{\text{human}}-A^*_{\text{flat}}.$$0 on OSWorld-Human (Abhyankar et al., 19 Jun 2025). 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 (Niaz et al., 2024, Sandrini et al., 2022, Lagomarsino et al., 2023, Sunbeam, 10 Nov 2025).

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 (Abhyankar et al., 19 Jun 2025). In program induction, a low action-efficiency ratio can reflect deliberate optimization of representational efficiency rather than poor problem solving (Sanborn et al., 2018). In contact-rich pHRI, no single scalar “efficiency” formula is defined; the most defensible interpretation is multicomponent and subtask-aware (Niaz et al., 2024). In synergy-based collaborative planning, estimated efficiency is contextual, directional, and overlap-dependent rather than intrinsic to an isolated task (Sandrini et al., 2022). In handovers, coefficiency uses normalized additive aggregation rather than a true relative ratio (Lagomarsino et al., 2023). 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 (Sunbeam, 10 Nov 2025).

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 (Sanborn et al., 2018). In other domains, the relevant baseline is a human-determined minimal trajectory, and excess actions primarily matter because they amplify latency (Abhyankar et al., 19 Jun 2025). 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 (Niaz et al., 2024, Sandrini et al., 2022, Sunbeam, 10 Nov 2025).

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 $$\mathrm{RHAE}_{\text{regret}}=A_{\text{human}}-A^*_{\text{flat}}.$$1 for program-induction action counts (Sanborn et al., 2018) and $$\mathrm{RHAE}_{\text{regret}}=A_{\text{human}}-A^*_{\text{flat}}.$$2 for human-referenced computer-use steps (Abhyankar et al., 19 Jun 2025). 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 (Niaz et al., 2024, Sandrini et al., 2022, Lagomarsino et al., 2023, Sunbeam, 10 Nov 2025).