# On the analysis of inexact augmented Lagrangian schemes for misspecified conic convex programs

arXiv: https://arxiv.org/abs/1608.01879 · HTML: https://mlsanity.com/paper/1608.01879/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2016.

## Built on by (most cited first, 3 of 3)

- [Distributed Fractional Bayesian Learning for Adaptive Optimization](https://mlsanity.com/paper/2404.11354/) (2024)
- [Rate Analysis of Coupled Distributed Stochastic Approximation for Misspecified Optimization](https://mlsanity.com/paper/2404.13669/) (2024)
- [Simultaneous Learning and Optimization via Misspecified Saddle Point Problems](https://mlsanity.com/paper/2510.05241/) (2025)

## Abstract (arXiv)

We consider the misspecified optimization problem of minimizing a convex function f(x;θ^*) in x over a conic constraint set represented by h(x;θ^*) ∈ K, where θ^* is an unknown (or misspecified) vector of parameters, K is a closed convex cone and h is affine in x. Suppose θ^* is unavailable but may be learnt by a separate process that generates a sequence of estimators θk, each of which is an increasingly accurate approximation of θ^*. We develop a first-order inexact augmented Lagrangian (AL) scheme for computing an optimal solution x^* corresponding to θ^* while simultaneously learning θ^*. In particular, we derive rate statements for such schemes when the penalty parameter sequence is either constant or increasing, and derive bounds on the overall complexity in terms of proximal-gradient steps when AL subproblems are inexactly solved via an accelerated proximal-gradient scheme. Numerical results for a portfolio optimization problem with a misspecified covariance matrix suggest that these schemes perform well in practice while naive sequential schemes may perform poorly in comparison.