Haoyuan Cai

Haoyuan Cai, Tengyu Ma, Simon Du · stanford

We revisit the incremental autonomous exploration problem proposed by Lim & Auer (2012). In this setting, the agent aims to learn a set of near-optimal goal-conditioned policies to reach the $L$-controllable states: states that are incrementally reachable from an initial state $s_0$ within $L$ steps in expectation. We introduce a new algorithm with stronger sample complexity bounds than existing ones. Furthermore, we also prove the first lower bound for the autonomous exploration problem. In particular, the lower bound implies that our proposed algorithm, Value-Aware Autonomous Exploration, is nearly minimax-optimal when the number of $L$-controllable states grows polynomially with respect to $L$. Key in our algorithm design is a connection between autonomous exploration and multi-goal stochastic shortest path, a new problem that naturally generalizes the classical stochastic shortest path problem. This new problem and its connection to autonomous exploration can be of independent interest.

Haoyuan Cai, Qi Ye, Dong-Ling Deng

Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to learn a parametric quantum circuit with at most $n^c$ gates and each gate acting on a constant number of qubits, the sample complexity is bounded by $\tilde{O}(n^{c+1})$. In particular, we explicitly construct a family of variational quantum circuits with $O(n^{c+1})$ elementary gates arranged in a fixed pattern, which can represent all physical quantum circuits consisting of at most $n^c$ elementary gates. Our results provide a valuable guide for quantum machine learning in both theory and practice.