Research map / Learning theory and algorithms / Sample complexity
Statistical Cost Sharing
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Compute balanced cost shares that satisfy the core on observed samples, then generalize with a VC-dimension bound | Games with a non-empty core · Distribution over coalitions | sample complexity for probably stable core: O\left(\frac{n + \log(1/ \Delta)}{\delta^2}\right) | Helped |
| Use bounded-\ell_1 cost shares and Rademacher complexity instead of the VC-based guarantee | Probably stable core algorithm · Games with a non-empty core | sample complexity dependence on n: linear to logarithmic | Helped |
| Require approximate stability for every coalition rather than probably approximate stability over sampled coalitions | Core computation from samples · Monotone submodular functions, uniform distribution | approximately stable core guarantee: (1/2 + \epsilon) | Hurt |
| Estimate the Shapley value with expected marginal contribution under the sample distribution | Monotone submodular functions with bounded curvature · Uniform distribution | Shapley value approximation factor: \sqrt{1-\kappa}-\epsilon | Helped |
| Estimate the Shapley value with expected marginal contribution under the sample distribution | Monotone submodular functions with bounded curvature · Bounded product distribution | Shapley value approximation factor: 1 - \kappa-\epsilon | Helped |
| Use a sampling distribution matching the Shapley permutation representation | Traditional Shapley value estimation · Shapley distribution | Shapley value approximation factor: (1 - \epsilon) | Helped |
| Use ordinary uniform-distribution samples to estimate the traditional Shapley value | Coverage functions · Uniform distribution | Shapley value approximation factor: no constant \alpha > 0 | Hurt |
| Replace the traditional Shapley value with the distribution-dependent value that splits each observed coalition cost equally among its members | Cost sharing from samples · Any bounded function and any distribution | data-dependent Shapley value estimation error: |\tilde{\phi}^{\mathcal{D}}_i - \phi^{\mathcal{D}}_i| < \epsilon | Helped |
| Estimate shares from conditional average costs of samples containing and excluding each player | Additive functions · Bounded product distributions | Shapley value and core approximation factor: (1-\epsilon) | Helped |
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