skscope: Fast Sparsity-Constrained Optimization in Python

Applying iterative solvers on sparsity-constrained optimization (SCO) requires tedious mathematical deduction and careful programming/debugging that hinders these solvers' broad impact. In the paper, the library skscope is introduced to overcome such an obstacle. With skscope, users can solve the SCO by just programming the objective function. The convenience of skscope is demonstrated through two examples in the paper, where sparse linear regression and trend filtering are addressed with just four lines of code. More importantly, skscope's efficient implementation allows state-of-the-art solvers to quickly attain the sparse solution regardless of the high dimensionality of parameter space. Numerical experiments reveal the available solvers in skscope can achieve up to 80x speedup on the competing relaxation solutions obtained via the benchmarked convex solver. skscope is published on the Python Package Index (PyPI) and Conda, and its source code is available at: https://github.com/abess-team/skscope.

Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models

We study the problem of off-policy evaluation (OPE) for episodic Partially Observable Markov Decision Processes (POMDPs) with continuous states. Motivated by the recently proposed proximal causal inference framework, we develop a non-parametric identification result for estimating the policy value via a sequence of so-called V-bridge functions with the help of time-dependent proxy variables. We then develop a fitted-Q-evaluation-type algorithm to estimate V-bridge functions recursively, where a non-parametric instrumental variable (NPIV) problem is solved at each step. By analyzing this challenging sequential NPIV problem, we establish the finite-sample error bounds for estimating the V-bridge functions and accordingly that for evaluating the policy value, in terms of the sample size, length of horizon and so-called (local) measure of ill-posedness at each step. To the best of our knowledge, this is the first finite-sample error bound for OPE in POMDPs under non-parametric models.

Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding

Data-driven individualized decision making has recently received increasing research interests. Most existing methods rely on the assumption of no unmeasured confounding, which unfortunately cannot be ensured in practice especially in observational studies. Motivated by the recent proposed proximal causal inference, we develop several proximal learning approaches to estimating optimal individualized treatment regimes (ITRs) in the presence of unmeasured confounding. In particular, we establish several identification results for different classes of ITRs, exhibiting the trade-off between the risk of making untestable assumptions and the value function improvement in decision making. Based on these results, we propose several classification-based approaches to finding a variety of restricted in-class optimal ITRs and develop their theoretical properties. The appealing numerical performance of our proposed methods is demonstrated via an extensive simulation study and one real data application.