arxiv: 2605.12646 · v1 · submitted 2026-05-12 · 💻 cs.LG · cs.AI· cs.HC

Recognition: no theorem link

Learning to Decide with AI Assistance under Human-Alignment

Nina Corvelo Benz , Eleni Straitouri , Manuel Gomez-Rodriguez

Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:40 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.HC

keywords AI-assisted decision makingonline learningregret boundshuman-AI alignmentconfidence calibrationcontextual banditsDvoretzky-Kiefer-Wolfowitz inequality

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The pith

Under perfect AI-human confidence alignment, expected regret for learning binary decisions drops to O(√(|H| T log T)).

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

The paper shows that deciding with AI assistance in binary tasks is equivalent to a two-armed online contextual learning problem with full feedback. In general this yields a lower bound of Ω(√(|H| |B| T)) on expected regret, where H and B are the sets of human and AI confidence values. When the AI and human confidence sets are perfectly aligned, the bound improves to O(√(|H| T log T)), and under the additional condition that √|H| grows like O(log T) with B countable, a generalized Dvoretzky-Kiefer-Wolfowitz inequality tightens it further to O(√(T log T)). These results matter because they quantify how alignment lowers the sample complexity of learning when to trust the AI through repeated interactions. Experiments on real human-subject data indicate the improved bounds remain informative even when alignment is only approximate.

Core claim

In the canonical binary prediction and decision setting, the decision-making problem with AI assistance reduces to online contextual learning with two actions and full feedback. Without alignment, any learner suffers expected regret at least Ω(√(|H| |B| T)), where H and B are the finite sets of possible human and AI confidence values. Under the assumption of perfect alignment—where the AI and human use the same set of confidence values—the regret improves to O(√(|H| T log T)). Moreover, when √|H| = O(log T) and the AI confidence set B is countable, a non-trivial generalization of the Dvoretzky–Kiefer–Wolfowitz inequality yields an even tighter bound of O(√(T log T)).

What carries the argument

The reduction of AI-assisted binary decision-making to a two-armed online contextual learning problem with full feedback, together with the perfect-alignment assumption that equates the human and AI confidence sets and thereby collapses the effective state space.

If this is right

Alignment removes the dependence on the size of the AI confidence set B from the leading term of the regret bound.
When the human confidence set H grows slowly, the regret bound approaches the no-AI baseline up to logarithmic factors.
The improved bounds continue to hold when the AI confidence set is countably infinite, provided |H| remains small.
Real-data experiments confirm that the theoretical improvement persists under moderate violations of perfect alignment.

Where Pith is reading between the lines

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

AI systems intended for decision assistance should be designed so their reported confidence values use the same discrete scale that humans naturally employ.
In settings where humans can distinguish only a few confidence levels, AI assistance can be learned to near-optimal performance with far fewer interactions than the general bound suggests.
The same alignment mechanism may extend to multi-class or continuous-action decisions, though the precise regret scaling would require a separate analysis.
Interface designers could actively encourage alignment by training users or by dynamically adjusting the AI's output granularity to match observed human behavior.

Load-bearing premise

The sets of AI confidence values and human confidence values in their own predictions must coincide exactly.

What would settle it

Measure the empirical regret curve in a repeated binary decision task where the AI and human confidence values are drawn from deliberately mismatched sets and check whether the growth rate matches the general lower bound Ω(√(|H| |B| T)) instead of the aligned upper bound.

Figures

Figures reproduced from arXiv: 2605.12646 by Eleni Straitouri, Manuel Gomez-Rodriguez, Nina Corvelo Benz.

**Figure 2.** Figure 2: Probability P(Y = 1 | H = h, B = b) vs AI confidence b given human confidence h for each group in the the Human-Alignment dataset (left) in the Human-AI Interactions dataset (right). Each line corresponds to the empirical value of P(Y = 1 | H = h, B = b) for a fixed value of h against values of b. Shaded areas represent 95% confidence intervals. 5 Discussion and Limitations In this section, we highlight se… view at source ↗

read the original abstract

It is widely agreed that when AI models assist decision-makers in high-stakes domains by predicting an outcome of interest, they should communicate the confidence of their predictions. However, empirical evidence suggests that decision-makers often struggle to determine when to trust a prediction based solely on this communicated confidence. In this context, recent theoretical and empirical work suggests a positive correlation between the utility of AI-assisted decision-making and the degree of alignment between the AI confidence and the decision-makers' confidence in their own predictions. Crucially, these findings do not yet elucidate the extent to which this alignment influences the complexity of learning to make optimal decisions through repeated interactions. In this paper, we address this question in the canonical case of binary predictions and binary decisions. We first show that this problem is equivalent to a two-armed online contextual learning problem with full feedback, and establish a lower bound of $\Omega (\sqrt{|H| \cdot |B| \cdot T} )$ on the expected regret any learner can attain, where $H$ and $B$ denote the sets of human and AI confidence values. We then demonstrate that, under perfect alignment between AI and human confidence, a learner can attain an expected regret of $O(\sqrt{|H| \cdot T\log T})$ and, when $\sqrt{|H|} = O(\log T)$ and $B$ is countable, a non-trivial generalization of the Dvoretzky-Kiefer-Wolfowitz inequality improves the regret bound to $O(\sqrt{T\log T})$. Taken together, these results reveal that alignment can reduce the complexity of learning to make decisions with AI assistance. Experiments on real data from two different human-subject studies where participants solve simple decision-making tasks assisted by AI models show that our theoretical results are robust to violations of perfect alignment.

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.

Desk Editor's Note private letter to a colleague

The paper's main contribution is a set of regret bounds that improve under human-AI confidence alignment in a bandit model of assisted decisions.

read the letter

The key point is that this paper demonstrates how alignment in confidence reporting between AI and humans can lower the regret bound for learning optimal decisions over repeated interactions, from something scaling with the product of their confidence set sizes down to scaling with just the human's. They model the binary decision task as a two-armed contextual bandit with full feedback, where the context is the pair of confidence values from human and AI. This leads to a general lower bound of Omega(sqrt(|H| |B| T)). But when the confidence sets align perfectly, the state space collapses and they derive an upper bound of O(sqrt(|H| T log T)). In the special case where the human set size grows slowly with T and the AI set is countable, they apply a generalized DKW inequality to get O(sqrt(T log T)). These bounds are new and come from applying standard online learning techniques to the aligned case. The paper does a good job keeping the analysis straightforward and tying it back to the empirical observations about alignment improving utility. The experiments using data from two human-subject studies provide some evidence that the findings are not too sensitive to small violations of perfect alignment. The main limitation is that the strongest results require perfect alignment, which is unlikely in real deployments. While the robustness experiments help, they don't replace a more general analysis that accounts for partial alignment. The math itself looks solid with no obvious errors in the derivations. This work is aimed at researchers studying human-AI teams in sequential decision settings. It offers useful theoretical insight into the long-term effects of alignment. I would recommend sending it for peer review; the contribution is clear and the evidence supports the claims without major gaps.

Referee Report

0 major / 2 minor

Summary. The paper models the problem of learning to make binary decisions with AI assistance as equivalent to two-armed online contextual learning with full feedback. It derives a general lower bound of Ω(√(|H| · |B| · T)) on expected regret, shows that perfect alignment between the human confidence set H and AI confidence set B yields an upper bound of O(√(|H| · T log T)), and further improves this to O(√(T log T)) when √|H| = O(log T) and B is countable via a generalized Dvoretzky-Kiefer-Wolfowitz inequality. Real human-subject experiments are used to check robustness under imperfect alignment.

Significance. If the results hold, this work quantifies the benefit of human-AI confidence alignment in reducing the sample complexity of learning optimal decision policies, with the regret bounds providing a clear theoretical separation between the aligned and unaligned cases. The clean reduction to standard online-learning analysis, the parameter-free derivations, and the application of concentration inequalities are strengths; the real-data experiments add practical relevance by showing the bounds remain informative even when perfect alignment is violated.

minor comments (2)

[Abstract] Abstract: the phrase 'non-trivial generalization of the Dvoretzky-Kiefer-Wolfowitz inequality' is used without a brief inline description or pointer to the precise form employed in the proof; adding one sentence would improve accessibility.
[Experiments] The experimental section would benefit from an explicit statement of the number of participants and trials per study when reporting robustness under imperfect alignment, to allow direct comparison with the T scaling in the bounds.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending acceptance. Their summary correctly captures the core technical contributions, including the reduction to two-armed online contextual learning, the general lower bound, the improved upper bounds under perfect alignment, and the robustness checks via human-subject experiments.

Circularity Check

0 steps flagged

No significant circularity; bounds derived from standard online-learning analysis on modeled equivalence

full rationale

The derivation begins by establishing an equivalence between the AI-assisted binary decision problem and a two-armed contextual bandit with full feedback (standard reduction, no self-reference). The lower bound Ω(√(|H| |B| T)) follows directly from known minimax results for contextual bandits once the joint state space is defined. Under the perfect-alignment assumption the joint space collapses to |H| states, after which the O(√(|H| T log T)) upper bound is obtained by applying any standard no-regret algorithm (e.g., EXP3 or UCB) whose analysis is independent of the present paper. The further O(√(T log T)) improvement when √|H| = O(log T) and B countable is a direct application of a generalized Dvoretzky–Kiefer–Wolfowitz concentration inequality to the reduced problem; the inequality itself is an external probabilistic fact. No quantity is defined in terms of a fitted parameter that is later treated as a prediction, no self-citation is load-bearing for the central claim, and no ansatz or renaming occurs. The derivation is therefore self-contained against external benchmarks in online learning.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard online-learning assumptions and the binary decision setting; no free parameters are introduced or fitted, and no new entities are postulated.

axioms (1)

domain assumption The human-AI decision problem is equivalent to a two-armed online contextual learning problem with full feedback.
This equivalence is invoked to import regret bounds from the online-learning literature.

pith-pipeline@v0.9.0 · 5634 in / 1286 out tokens · 49242 ms · 2026-05-14T21:40:32.356126+00:00 · methodology

discussion (0)

Reference graph

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13 A Proofs A.1 Proof of Theorem 1 Our proof closely follows the proof of Theorem 5.1 in Agarwal et al. (2012) that shows that learning the optimal policy π∗ for the contextual multi-armed bandit problem with a policy classΠandK arms (refer to Slivkins (2019) Chapter 8.4 for the exact definition) has expected regretE(R(T )) = Ω p K·T·log(|Π|)/log(K) , as ...

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Proof.Similar to Lemma A.1 Auer et al

4 , whereE i,E unif denote the expectation with respect to the distributionPi andP unif respectively. Proof.Similar to Lemma A.1 Auer et al. (2002) we have Ei[f(R)]−E unif[f(R)] = X R f(R)(P i[R]−P unif[R])≤M· X R (Pi[R]−P unif[R]) ≤M· X R:Pi[R]≥Punif[R] (Pi[R]−P unif[R]) = M 2 ||Pi −P unif ||1,(11) where||P i −P unif ||1 is the variational distance betwe...

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4 Note that the above bound no longer depends on the expected number of times that the algorithm chose to play the armias in Auer et al. (2002). We will use the above result to prove Corollary 7 below, in the context of the construction used by Agarwal et al. (2012), which we restate for completeness: We assumeM different contexts, a policy classΠcomprisi...

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[12]

(2012) we have that the expected regret E[R(T)] = Ω M·ϵ− ϵ2 √ M ·T 3/2 , which forϵ= Θ( p M/T)becomes E[R(T)] = Ω √ T·M = Ω s T· log(|Π|) logK !

By using Corollary 7 instead of Corollary 5.1 in the rest of the proof by Agarwal et al. (2012) we have that the expected regret E[R(T)] = Ω M·ϵ− ϵ2 √ M ·T 3/2 , which forϵ= Θ( p M/T)becomes E[R(T)] = Ω √ T·M = Ω s T· log(|Π|) logK ! . Since|Π|=K |H|·|B| we have E[R(T)] = Ω p T· |H|·|B| A.2 Proof of Theorem 2 Leth∈ H. Due to perfect alignment, for anyb, b...

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[13]

(1956); Massart (1990)) Given a natural numbern, let Z1, Z2,

Then, we show that under perfect alignment, our algorithm’s expected regret on the|H|independent instances of the multi-armed online learning problem is equivalent to its expected regret on the two-armed online contextual learning problem with full feedback Theorem 8.(DKW inequality Dvoretzky et al. (1956); Massart (1990)) Given a natural numbern, let Z1,...

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[14]

TX t=1 µ(ℓ∗)−µ( ¯ℓt)| E # +P(E c)·E ¯ℓt∼P( ¯ℓt)

> c 3 p |H|, that is, when p |H|< c 4 log(T )for some c4 > 0( c4 equals constant c in the statement of the theorem). We can now rewrite and bound the expected utility conditional on this event as E[R(T)] =P(E)·E ¯ℓt∼P( ¯ℓt) " TX t=1 µ(ℓ∗)−µ( ¯ℓt)| E # +P(E c)·E ¯ℓt∼P( ¯ℓt) " TX t=1 µ(ℓ∗)−µ( ¯ℓt)| E c # ≤E ¯ℓt∼P( ¯ℓt) " TX t=1 µ(ℓ∗)−µ( ¯ℓt)| E # +P(E c)·T ...

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Definition 12(VC Dimension Sen (2018)).Given a function classF of binary-valued functions, we say that the set{x 1,

Then, for allϵ≥0 P(Z≥E[Z] +ϵ)≤exp − νn U2 h1 ϵU νn ≤exp −ϵ2 2νn + 2ϵU/3 (46) whereh 1(w) = (1 +w) log(1 +w)−wforw∈Rand P(Z≥E[Z] + p 2νnδ+U δ/3)≤e −δ, δ≥0. Definition 12(VC Dimension Sen (2018)).Given a function classF of binary-valued functions, we say that the set{x 1, . . . , xn}is shattered byFif |F(x1, . . . , xn)|= 2n whereF(x 1, . . . , xn) ={(f(x 1...

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[16]

Then, there exist constantc1 >0such that for anyϵ > c 1 p |K|/n P   sup ∆∈D 1 n X i∈[n] ∆(Ki, Xi)−E K,X∼P(K,X) [∆(K, X)] > ϵ   ≤exp − nϵ2 4c2 p |K| ! for some constantc2 > c1. Proof. This proof closely follows the proof of the DKW inequality for outcome spaceRd outlined in Sen (2018). LetZbe as in Lemma

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[17]

Then, there exist constantc1 >0such that for anyϵ > c 1 p |K|/n P   sup ∆+∈D+ 1 n X i∈[n] ∆+(Ki, Xi)−E K,X∼P(K,X) [∆+(K, X)] > ϵ   ≤exp − nϵ2 4c2 p |K| ! for some constantc2 > c1. 32 Proof.First, note that, for any∆∈ D, we have that 1 n X i∈[n] ∆(Ki, Xi)−E K,X∼P(K,X) [∆(K, X)] = −1 + 1 n X i∈[n] ∆(Ki, Xi)) + 1−E K,X∼P(K,X) [∆(K, X)] = −   1 n X i∈[n...

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[18]

Further, we clarify that in the Human-Alignment dataset the game-specific parameterq denotes the fraction of red cards in the card pile shown to participants

The Human-Alignment dataset is publicly available under GNU General Public License v3.0 and Human-AI Interactions dataset is publicly available under MIT License. Further, we clarify that in the Human-Alignment dataset the game-specific parameterq denotes the fraction of red cards in the card pile shown to participants. For more details and the exact card...

work page 2025