Computational complexity of tight partial-identification bounds

Determine whether computing tight causal bounds for general (e.g., multi-valued or continuous) treatments and outcomes is solvable in polynomial time or is computationally hard; characterize the complexity landscape of partial identification.

Background

While binary cases reduce to small linear programs, more general settings cause combinatorial growth in the response-type polytope.

The authors ask whether there exist efficient algorithms in general or whether the problem becomes intractable, noting that the quantum analogue is undecidable but the classical case may be more tractable.

References

The unified framework raises several open questions that span the boundaries of quantum information, causal inference, and statistical computation. Is there a polynomial-time algorithm for computing tight causal bounds in general, or does partial identification become computationally hard for large problems? The connection to MIP$*$=RE suggests that the quantum version is undecidable, but the classical version may have a more favorable complexity landscape.

— Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework  (2603.28973 - Polson et al., 30 Mar 2026) in Section 7, Open Problems