arXiv subjects

Jincheng Mei

Publications and source records attributed to Jincheng Mei.

22 records · Page 2Linked to original sources

arXiv2021

On the Optimality of Batch Policy Optimization Algorithms

Batch policy optimization considers leveraging existing data for policy construction before interacting with an environment. Although interest in this problem has grown significantly in recent years, its theoretical foundations remain under-developed. To advance the understanding of this problem, we provide three results that characterize the limits and possibilities of batch policy optimization in the finite-armed stochastic bandit setting. First, we introduce a class of confidence-adjusted index algorithms that unifies optimistic and pessimistic principles in a common framework, which enables a general analysis. For this family, we show that any confidence-adjusted index algorithm is minimax optimal, whether it be optimistic, pessimistic or neutral. Our analysis reveals that instance-dependent optimality, commonly used to establish optimality of on-line stochastic bandit algorithms, cannot be achieved by any algorithm in the batch setting. In particular, for any algorithm that performs optimally in some environment, there exists another environment where the same algorithm suffers arbitrarily larger regret. Therefore, to establish a framework for distinguishing algorithms, we introduce a new weighted-minimax criterion that considers the inherent difficulty of optimal value prediction. We demonstrate how this criterion can be used to justify commonly used pessimistic principles for batch policy optimization.

cs.LG↗

arXiv2020

Frequency-based Search-control in Dyna

Model-based reinforcement learning has been empirically demonstrated as a successful strategy to improve sample efficiency. In particular, Dyna is an elegant model-based architecture integrating learning and planning that provides huge flexibility of using a model. One of the most important components in Dyna is called search-control, which refers to the process of generating state or state-action pairs from which we query the model to acquire simulated experiences. Search-control is critical in improving learning efficiency. In this work, we propose a simple and novel search-control strategy by searching high frequency regions of the value function. Our main intuition is built on Shannon sampling theorem from signal processing, which indicates that a high frequency signal requires more samples to reconstruct. We empirically show that a high frequency function is more difficult to approximate. This suggests a search-control strategy: we should use states from high frequency regions of the value function to query the model to acquire more samples. We develop a simple strategy to locally measure the frequency of a function by gradient and hessian norms, and provide theoretical justification for this approach. We then apply our strategy to search-control in Dyna, and conduct experiments to show its property and effectiveness on benchmark domains.

cs.LG↗

arXiv2016

On the Reducibility of Submodular Functions

The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular optimization problems without performance loss. We introduce the concept of reducibility using marginal gains. Then we show that by adding perturbation, we can endow irreducible functions with reducibility, based on which we propose the perturbation-reduction optimization framework. Our theoretical analysis proves that given the perturbation scales, the reducibility gain could be computed, and the performance loss has additive upper bounds. We further conduct empirical studies and the results demonstrate that our proposed framework significantly accelerates existing optimization methods for irreducible submodular functions with a cost of only small performance losses.

cs.LG↗

arXiv2014

On Unconstrained Quasi-Submodular Function Optimization

With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which satisfies weaker properties than submodularity but still enjoys favorable performance in optimization. Similar to the diminishing return property of submodularity, we first define a corresponding property called the {\em single sub-crossing}, then we propose two algorithms for unconstrained quasi-submodular function minimization and maximization, respectively. The proposed algorithms return the reduced lattices in $\mathcal{O}(n)$ iterations, and guarantee the objective function values are strictly monotonically increased or decreased after each iteration. Moreover, any local and global optima are definitely contained in the reduced lattices. Experimental results verify the effectiveness and efficiency of the proposed algorithms on lattice reduction.

cs.DS↗