Explainable machine learning (ML) has gained traction in recent years due to the increasing adoption of ML-based systems in many sectors. Counterfactual explanations (CFEs) provide ``what if feedback of the form ``if an input datapoint were $x$ instead of $x$, then an ML-based systems output would be $y$ instead of $y$. CFEs are attractive due to their actionable feedback, amenability to existing legal frameworks, and fidelity to the underlying ML model. Yet, current CFE approaches are single shot -- that is, they assume $x$ can change to $x$ in a single time period. We propose a novel stochastic-control-based approach that generates sequential CFEs, that is, CFEs that allow $x$ to move stochastically and sequentially across intermediate states to a final state $x$. Our approach is model agnostic and black box. Furthermore, calculation of CFEs is amortized such that once trained, it applies to multiple datapoints without the need for re-optimization. In addition to these primary characteristics, our approach admits optional desiderata such as adherence to the data manifold, respect for causal relations, and sparsity -- identified by past research as desirable properties of CFEs. We evaluate our approach using three real-world datasets and show successful generation of sequential CFEs that respect other counterfactual desiderata.
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