  The ability to differentiate through optimization problems has unlocked
numerous applications, from optimization-based layers in machine learning
models to complex design problems formulated as bilevel programs. It has been
shown that exploiting problem structure can yield significant computation gains
for optimization and, in some cases, enable distributed computation. One should
expect that this structure can be similarly exploited for gradient computation.
In this work, we discuss a decentralized framework for computing gradients of
constraint-coupled optimization problems. First, we show that this framework
results in significant computational gains, especially for large systems, and
provide sufficient conditions for its validity. Second, we leverage exponential
decay of sensitivities in graph-structured problems towards building a fully
distributed algorithm with convergence guarantees. Finally, we use the
methodology to rigorously estimate marginal emissions rates in power systems
models. Specifically, we demonstrate how the distributed scheme allows for
accurate and efficient estimation of these important emissions metrics on large
dynamic power system models.
