Price of Explainability (PoE) in AI Models

• PoE is a metric that quantifies the trade-off cost imposed by enforcing explainability constraints across various AI decision-making and modeling contexts.
• It captures diverse formalizations, including ratio-based losses in Bayesian persuasion, explainable clustering, and path-based interpretability, each with unique structural constraints.
• The metric informs both algorithmic performance and socio-technical considerations by balancing accuracy, computational cost, fairness, and privacy in explainable AI systems.

Searching arXiv for the cited PoE papers to ground the article in the latest literature. Price of Explainability (PoE) denotes the loss, cost, or trade-off induced by imposing an explainability constraint on an otherwise unconstrained decision, model, clustering, signaling policy, or explanation pipeline. The term does not have a single universal formalization. In current arXiv literature, PoE appears as a worst-case ratio between explainable and unrestricted objectives in Bayesian persuasion and clustering, as an accuracy loss under an interpretability budget in model construction, as a nominal-cost increase in data-driven mathematical optimization, and as a monetary, welfare, fairness, privacy, or computational trade-off in explainable AI systems (Chen et al., 19 Aug 2025, Gupta et al., 2023, Bertsimas et al., 2019, Aigner et al., 2023, Greene et al., 2023, Mikriukov et al., 31 Mar 2026).

1. Major formalizations

Different research programs operationalize explainability through different structural constraints. In Bayesian persuasion, explainability means deterministic monotone partitions of a one-dimensional state space. In explainable clustering, it means axis-aligned threshold trees. In path-based interpretability, it means constructing a model through interpretable steps. In data-driven mathematical optimization, it means similarity to historically implemented solutions. In monetized and cost-aware XAI, it refers to the economic or computational consequences of producing explanations (Chen et al., 19 Aug 2025, Gupta et al., 2023, Bertsimas et al., 2019, Aigner et al., 2023, Greene et al., 2023, Mikriukov et al., 31 Mar 2026).

Setting	Explainability constraint	Representative PoE definition
Information design	$K$-partitional, deterministic, monotone signaling	$$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$
Clustering	Axis-aligned threshold tree with $k$ leaves	$$\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$$
Path-based interpretability	Interpretable-step paths in model space	$\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$
Data-driven optimization	Similarity to historical solutions	$$\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$$
Monetized XAI	Explanation platform with ads	$\mathrm{PoE}_{\$} = R_{\text{with monetized XAI}}-R_{\text{without monetized XAI}}$$</td> </tr> <tr> <td>Cost-aware post-hoc XAI</td> <td>Routing or deferral under budget</td> <td>$$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$</td> </tr> </tbody></table></div> <p>These formalizations differ in both numerator and denominator. Some are ratio-based and worst-case, some are additive and instance-specific, and some are explicitly multiobjective. The common element is that explainability is not treated as free: it is enforced by a constraint, and the induced degradation or reallocation is then quantified.</p> <h2 class='paper-heading' id='bayesian-persuasion-and-explainable-information-design'>2. Bayesian persuasion and explainable information design</h2> <p>In “<a href="https://www.emergentmind.com/topics/explainable-information-design" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Explainable Information Design</a>,” the state space is one-dimensional, typically$$\Theta=[0,1]$, with prior$F$having continuous density$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$0 and full support on $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$1. The sender’s interim payoff depends only on the posterior mean $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$2 through an upper-semicontinuous utility $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$3. Unrestricted signaling is represented by mean-preserving contractions (MPCs) of the prior, while explainable signaling is restricted to $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$4-partitional signaling schemes defined by deterministic and monotone partitions of the state space, where a unique signal is sent for all states in each part (Chen et al., 19 Aug 2025). For a signaling scheme $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$5, the expected sender utility is $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$6 where $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$7 is the MPC induced by $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$8. For a $\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$9-partitional policy with partition points $k$0, $k$1 The paper defines $k$2 Its central theorem is a tight worst-case guarantee: for every instance with continuous one-dimensional state and every $k$3, $k$4, and for every $k$5 there exists an instance with $k$6. Hence the worst-case price of explainability is exactly $k$7 (Chen et al., 19 Aug 2025). In this formulation, explainable partitional signaling schemes are never worse than arbitrary signaling schemes by a factor of $k$8. The structural mechanism behind the bound is the bi-pooling property. Optimal unrestricted $k$9-signal schemes can be taken to be extreme points of the feasible MPC set, and these extreme points are bi-pooling schemes without full revelation intervals. On each interval, the unrestricted scheme uses either one posterior mean or two posterior means $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$0 satisfying $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$1 A technical conversion refines each bi-pooling interval into a contiguous partition that achieves at least $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$2 and summing across intervals yields a $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$3-partitional scheme with value at least $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$4. The computational picture is mixed. Exact optimization of the best $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$5-partitional scheme is NP-hard, even when $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$6 is piecewise-linear and $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$7-Lipschitz or binary-valued. Under Lipschitz and boundedness assumptions on $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$8 and bounded density $\mathrm{PoE}_k = \sup_X \frac{\mathrm{cost}(\text{best explainable }k\text{-clustering})}{\mathrm{cost}(\text{best unconstrained }k\text{-clustering})}$9, the paper gives an FPTAS based on discretization and dynamic programming. For piecewise-constant utility functions, it gives a polynomial-time procedure that computes a $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$0-partitional scheme achieving a $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$1 approximation to the optimal unrestricted $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$2-signal scheme, matching the worst-case PoE bound. The same paper also notes that in special cases such as convex, concave, and S-shaped $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$3, partitional schemes are optimal among $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$4-signal schemes, so $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$5 (Chen et al., 19 Aug 2025). 3. Explainable clustering and decision-tree partitions In clustering, explainability is typically enforced through axis-aligned threshold trees. A threshold cut has the form $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$6, and a threshold tree induces a partition of $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$7 into axis-aligned boxes whose intersections with the dataset are the explainable clusters. In this setting, $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$8 for minimization objectives such as $\mathrm{PoE}(\ell) := c(m_\ell)-c(m^*)$9-medians and $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$0-means (Gupta et al., 2023). For $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$1-medians, the current sharp worst-case upper bound is $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$2 where $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$3. The same paper proves that the Random Thresholds algorithm has exactly this price of explainability, matching known lower bound constructions, and shows that any explainable clustering can have cost at least $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$4 times the optimal unconstrained cost. For $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$5-means, it improves the upper bound to $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$6 from the previous $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$7, while the lower bound remains $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$8 (Gupta et al., 2023). The algorithmic hardness is also explicit. Unless $\mathrm{PoE}(\tau) := C(x^{\mathrm{exp}_\tau})-C(x^{\mathrm{opt}})$9, explainable $\mathrm{PoE}_{\$0-medians and $\mathrm{PoE}_{\$1-means cannot be approximated within a factor better than $\mathrm{PoE}_{\$2. This essentially settles the approximability of explainable $\mathrm{PoE}_{\$3-medians and leaves open whether explainable $\mathrm{PoE}_{\$4-means admits approximation algorithms substantially better than its current worst-case PoE (Gupta et al., 2023). An earlier line of work studies the same decision-tree explainability model for several clustering objectives and derives dimension-sensitive bounds. Under this model, the price of explainability is $\mathrm{PoE}_{\$5 for $\mathrm{PoE}_{\$6-medians and $\mathrm{PoE}_{\$7 for $\mathrm{PoE}_{\$8-means, improving earlier ICML 2020 bounds in low dimensions. The same work gives $\mathrm{PoE}_{\$9 and proves that for maximum-spacing the price of explainability is $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$0. It also proposes Ex-Greedy, a practical algorithm for explainable $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$1-means, and reports empirical improvements over IMM on several datasets, including Mice, Digits, CIFAR-10, Anuran, and Avila (Laber et al., 2021). Taken together, these papers show that the combinatorial restriction “explainable by axis-aligned cuts” has sharply different consequences across objectives. For $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$2-medians the loss is logarithmic and essentially tight; for $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$3-means it is near-linear in $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$4 up to a $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$5 factor; for maximum-spacing it can be linear in $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$6. 4. Path-based interpretability and data-driven optimization A different formalization appears in “The Price of Interpretability,” where models are constructed through interpretable steps. Let $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$7 be the model space and $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$8 the predictive cost. An interpretable step is encoded by a neighborhood function $$\mathrm{PoE}(r) = \min_{\pi:\ \mathbb{E}[R(x,\pi(x))]\ge r}\ \mathbb{E}[C(\pi(x))]$$9, and an interpretable path is a sequence $\Theta=[0,1]$0 with $\Theta=[0,1]$1. The paper defines a coherent family of path losses $\Theta=[0,1]$2 and, for the geometric-weight family, $\Theta=[0,1]$3 The corresponding price of explainability at interpretability budget $\Theta=[0,1]$4 is $\Theta=[0,1]$5 where $\Theta=[0,1]$6 is the unconstrained accuracy-optimal model and $\Theta=[0,1]$7 solves $\Theta=[0,1]$8 subject to $\Theta=[0,1]$9 (Bertsimas et al., 2019). This framework recovers standard proxies. For linear models, path complexity yields sparsity $F$0; for CART it yields number of splits; for clustering it yields number of clusters. As $F$1, the loss prioritizes shorter minimal paths and, when lengths coincide, lower final predictive cost. As $F$2, it favors lexicographically better stepwise cost sequences, hence greedier incremental constructions. The paper also gives exact and heuristic optimization procedures, including MIO formulations for trees and SOS-1 formulations for linear regression (Bertsimas et al., 2019). In “A Framework for Data-Driven Explainability in Mathematical Optimization,” explainability is instead defined relative to historical decisions. Historical tuples $F$3 are filtered by an instance-similarity rule $F$4 and the explainability score is $F$5 The nominal objective is $F$6, and the explainable problem is treated as the multiobjective problem $F$7 or the weighted-sum scalarization $F$8 Its constrained PoE is $F$9 The general problem is NP-hard even with one historical instance, but polynomially solvable cases arise under Hamming-feature mappings, including explainable shortest path in DAGs and minimum spanning tree. Empirically, the paper reports that in synthetic road networks a nominal-cost increase of about $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$00 yields high explainability when solution features cover all edges, that fully explainable solutions can be obtained with an average $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$01 reduction in optimality when features are restricted to bridges, and that on a real Chicago road network fully explainable solutions require less than $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$02 increase in nominal cost (Aigner et al., 2023). 5. Monetary, welfare, fairness, and privacy prices A socio-technical interpretation appears in “Monetizing Explainable AI: A Double-edged Sword.” There, an explanation platform is defined as an enabling technology allowing third-parties to bid on the opportunity to place ads alongside algorithmic explanations. The platform bundles the automated decision, the selected explanation, and an ad, and exposes explanation inventory to real-time bidding. The paper explicitly treats the Price of Explainability in two senses: the monetary price or revenue generated by explanations, and the costs to performance, privacy, fairness, and welfare when explanations are provided and monetized (Greene et al., 2023). Its revenue model uses the standard formulas $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$03 Using CPC benchmarks, it estimates annual revenue potential of $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$04 for finance, approximately $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$05 for employment, and $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$06 for education. The same paper then simulates monetization strategies on the German Credit dataset using a Random Forest with test AUC $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$07 and DiCE counterfactuals. Extrapolated to $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$08 annual credit-card applications, the reported revenues are $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$09 for the baseline, $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$10 for feature picking, $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$11 for spam explanations, $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$12 for inflated rejection, and $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$13 for spam plus inflated rejection (Greene et al., 2023). The same work formalizes several PoE variants: $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$14 $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$15 $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$16 and fairness changes through $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$17 and $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$18, where $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$19 $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$20 This literature therefore uses PoE not as a single efficiency ratio but as a vector of gains and harms. Explanations can finance transparency and lower search costs for recourse, but they can also create incentives for threshold inflation, explanation multiplicity, privacy erosion, and manipulation. The paper frames this explicitly as a double-edged sword and connects the issue to GDPR, the EU AI Act, the DMA, the DSA, and the US AI Bill of Rights blueprint (Greene et al., 2023). 6. Computational PoE for post-hoc XAI and recurring themes “Uncertainty Gating for Cost-Aware Explainable Artificial Intelligence” studies the computational price of producing explanations with acceptable reliability. Its premise is that epistemic uncertainty is a low-cost proxy for explanation reliability: high epistemic uncertainty identifies regions where decision boundaries are poorly defined and where explanations become unstable and unfaithful. The paper proposes two use cases. In routing, a threshold $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$21 chooses between cheap and expensive explainers: $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$22 In budgeted deferral, only sufficiently certain samples are explained: $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$23 The paper defines $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$24 Its relative cost proxy is $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$25 On Dry Bean with RF+TreeSHAP, the reported cost–reliability points are $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$26 at $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$27, $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$28 at $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$29, and $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$30 at $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$31; on Rice they are $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$32 at $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$33 and $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$34 at $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$35. The paper emphasizes that the marginal price can be negative, because deferral may simultaneously increase reliability and decrease cost (Mikriukov et al., 31 Mar 2026). This computational interpretation differs from the structural and worst-case formulations, but it shares a common optimization pattern: choose an explainability policy under a resource or reliability constraint. The same work also reports that low $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$36 weakens the gating signal, that permutation shifts yield weaker XAI–UQ correlations, and that the framework is focused on classification, leaving regression and structured outputs for future work (Mikriukov et al., 31 Mar 2026). Across these literatures, explainability is repeatedly enforced through a structural restriction, a historical-similarity criterion, or a resource-allocation rule. This suggests that PoE is best understood as a family of trade-off functionals rather than a single invariant quantity. Some settings admit tight worst-case constants, such as the exact $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$37 bound for partitional information design and the exact $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$38 bound for explainable $$\mathrm{PoE}(I,K) := \frac{V^*_{\mathrm{exp}(K)}}{V^*_{\mathrm{unres}(K)}}$$39-medians (Chen et al., 19 Aug 2025, Gupta et al., 2023). Other settings are dominated by hardness results, feature-design dependence, or socio-technical externalities. The resulting landscape is therefore heterogeneous: PoE can be a sharp approximation ratio, an additive efficiency loss, an empirical Pareto frontier, or a vector of economic and normative costs. Topic to Video (Beta) No one has generated a video about this topic yet. 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Continue Learning How do the different formalizations of PoE compare across Bayesian persuasion, clustering, and path-based interpretability?  What are the primary computational challenges in optimizing models under explainability constraints?  In what ways does the introduction of explainability constraints impact the overall performance and accuracy of AI systems?  How can socio-technical factors like fairness, privacy, and monetization be integrated into the evaluation of PoE?  Find recent papers about explainable clustering trade-offs.  Related Topics Price of Equality in Efficiency Trade-offs  Cost-of-Pass: A Unified Resource Efficiency Metric  Rashomon Capacity: Model Multiplicity  Post-Hoc Robustification Design Patterns  Bounded Personalization Frameworks  Bounded Calibration with Contestability  Cost-Aware Policy Optimization (CAPO)  Explanatory Robustness (ER)  Consensus Preference Optimization Methods  Explainable Information Design  Content Overview References Topic to Video Whiteboard Follow Topic Continue Learning Related Topics Stay informed about trending AI papers: About Labs API Email Digest Chrome Extension RSS Terms Privacy Contact Twitter Discord