Spherical-coding discretization of the contract space

Determine a method from spherical coding in information theory that discretizes the contract space \(\mathcal{X}\) as required for implementing the cited adaptive contract-design algorithm.

Background

The paper reviews an earlier algorithm for the principal-agent problem that removes monotonicity and first-order stochastic-dominance assumptions but requires discretizing the continuous contract space X\mathcal{X} using methods from spherical coding in information theory. The authors state that this required discretization procedure remains unresolved, making the cited algorithm impossible to implement in practice. This problem is included because it is the only explicitly identified unresolved issue in the paper that is not itself resolved by the paper’s proposed stochastic reformulation and kernelized bandit method.

References

In fact, one of the steps in their algorithm requires $\mathcal{X}$ to be discretized using certain methods from spherical coding in information theory, which remains an open problem to date (Section $3.1$ of ).

— Adaptive Incentive Design in Dynamic Principal-Agent Problem via Kernelized Bandits  (2608.17614 - Mallick et al., 18 Aug 2026) in Section 2, subsection “State-of-the-art results” (discussion of the algorithm in \cite{zhu2023sample})