Hinge Policy Optimization: Rethinking Policy Improvement and Reinterpreting PPO

Policy optimization is a fundamental principle for designing reinforcement learning algorithms, and one example is the proximal policy optimization algorithm with a clipped surrogate objective (PPO-clip), which has been popularly used in deep reinforcement learning due to its simplicity and effectiveness. Despite its superior empirical performance, PPO-clip has not been justified via theoretical proof up to date. This paper proposes to rethink policy optimization and reinterpret the theory of PPO-clip based on hinge policy optimization (HPO), called to improve policy by hinge loss in this paper. Specifically, we first identify sufficient conditions of state-wise policy improvement and then rethink policy update as solving a large-margin classification problem with hinge loss. By leveraging various types of classifiers, the proposed design opens up a whole new family of policy-based algorithms, including the PPO-clip as a special case. Based on this construct, we prove that these algorithms asymptotically attain a globally optimal policy. To our knowledge, this is the first ever that can prove global convergence to an optimal policy for a variant of PPO-clip. We corroborate the performance of a variety of HPO algorithms through experiments and an ablation study.

NeurWIN: Neural Whittle Index Network For Restless Bandits Via Deep RL

Whittle index policy is a powerful tool to obtain asymptotically optimal solutions for the notoriously intractable problem of restless bandits. However, finding the Whittle indices remains a difficult problem for many practical restless bandits with convoluted transition kernels. This paper proposes NeurWIN, a neural Whittle index network that seeks to learn the Whittle indices for any restless bandits by leveraging mathematical properties of the Whittle indices. We show that a neural network that produces the Whittle index is also one that produces the optimal control for a set of Markov decision problems. This property motivates using deep reinforcement learning for the training of NeurWIN. We demonstrate the utility of NeurWIN by evaluating its performance for three recently studied restless bandit problems. Our experiment results show that the performance of NeurWIN is significantly better than other RL algorithms.

Reinforced Few-Shot Acquisition Function Learning for Bayesian Optimization

Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions. This paper aims to attack this challenge through the perspective of reinforced few-shot AF learning (FSAF). Specifically, we first connect the notion of AFs with Q-functions and view a deep Q-network (DQN) as a surrogate differentiable AF. While it serves as a natural idea to combine DQN and an existing few-shot learning method, we identify that such a direct combination does not perform well due to severe overfitting, which is particularly critical in BO due to the need of a versatile sampling policy. To address this, we present a Bayesian variant of DQN with the following three features: (i) It learns a distribution of Q-networks as AFs based on the Kullback-Leibler regularization framework. This inherently provides the uncertainty required in sampling for BO and mitigates overfitting. (ii) For the prior of the Bayesian DQN, we propose to use a demo policy induced by an off-the-shelf AF for better training stability. (iii) On the meta-level, we leverage the meta-loss of Bayesian model-agnostic meta-learning, which serves as a natural companion to the proposed FSAF. Moreover, with the proper design of the Q-networks, FSAF is general-purpose in that it is agnostic to the dimension and the cardinality of the input domain. Through extensive experiments, we demonstrate that the FSAF achieves comparable or better regrets than the state-of-the-art benchmarks on a wide variety of synthetic and real-world test functions.

Escaping from Zero Gradient: Revisiting Action-Constrained Reinforcement Learning via Frank-Wolfe Policy Optimization

Action-constrained reinforcement learning (RL) is a widely-used approach in various real-world applications, such as scheduling in networked systems with resource constraints and control of a robot with kinematic constraints. While the existing projection-based approaches ensure zero constraint violation, they could suffer from the zero-gradient problem due to the tight coupling of the policy gradient and the projection, which results in sample-inefficient training and slow convergence. To tackle this issue, we propose a learning algorithm that decouples the action constraints from the policy parameter update by leveraging state-wise Frank-Wolfe and a regression-based policy update scheme. Moreover, we show that the proposed algorithm enjoys convergence and policy improvement properties in the tabular case as well as generalizes the popular DDPG algorithm for action-constrained RL in the general case. Through experiments, we demonstrate that the proposed algorithm significantly outperforms the benchmark methods on a variety of control tasks.

Reward-Biased Maximum Likelihood Estimation for Linear Stochastic Bandits

Modifying the reward-biased maximum likelihood method originally proposed in the adaptive control literature, we propose novel learning algorithms to handle the explore-exploit trade-off in linear bandits problems as well as generalized linear bandits problems. We develop novel index policies that we prove achieve order-optimality, and show that they achieve empirical performance competitive with the state-of-the-art benchmark methods in extensive experiments. The new policies achieve this with low computation time per pull for linear bandits, and thereby resulting in both favorable regret as well as computational efficiency.

Developing Multi-Task Recommendations with Long-Term Rewards via Policy Distilled Reinforcement Learning

With the explosive growth of online products and content, recommendation techniques have been considered as an effective tool to overcome information overload, improve user experience, and boost business revenue. In recent years, we have observed a new desideratum of considering long-term rewards of multiple related recommendation tasks simultaneously. The consideration of long-term rewards is strongly tied to business revenue and growth. Learning multiple tasks simultaneously could generally improve the performance of individual task due to knowledge sharing in multi-task learning. While a few existing works have studied long-term rewards in recommendations, they mainly focus on a single recommendation task. In this paper, we propose {\it PoDiRe}: a \underline{po}licy \underline{di}stilled \underline{re}commender that can address long-term rewards of recommendations and simultaneously handle multiple recommendation tasks. This novel recommendation solution is based on a marriage of deep reinforcement learning and knowledge distillation techniques, which is able to establish knowledge sharing among different tasks and reduce the size of a learning model. The resulting model is expected to attain better performance and lower response latency for real-time recommendation services. In collaboration with Samsung Game Launcher, one of the world's largest commercial mobile game platforms, we conduct a comprehensive experimental study on large-scale real data with hundreds of millions of events and show that our solution outperforms many state-of-the-art methods in terms of several standard evaluation metrics.

Bandit Learning Through Biased Maximum Likelihood Estimation

We propose BMLE, a new family of bandit algorithms, that are formulated in a general way based on the Biased Maximum Likelihood Estimation method originally appearing in the adaptive control literature. We design the cost-bias term to tackle the exploration and exploitation tradeoff for stochastic bandit problems. We provide an explicit closed form expression for the index of an arm for Bernoulli bandits, which is trivial to compute. We also provide a general recipe for extending the BMLE algorithm to other families of reward distributions. We prove that for Bernoulli bandits, the BMLE algorithm achieves a logarithmic finite-time regret bound and hence attains order-optimality. Through extensive simulations, we demonstrate that the proposed algorithms achieve regret performance comparable to the best of several state-of-the-art baseline methods, while having a significant computational advantage in comparison to other best performing methods. The generality of the proposed approach makes it possible to address more complex models, including general adaptive control of Markovian systems.

Streaming Network Embedding through Local Actions

Recently, considerable research attention has been paid to network embedding, a popular approach to construct feature vectors of vertices. Due to the curse of dimensionality and sparsity in graphical datasets, this approach has become indispensable for machine learning tasks over large networks. The majority of existing literature has considered this technique under the assumption that the network is static. However, networks in many applications, nodes and edges accrue to a growing network as a streaming. A small number of very recent results have addressed the problem of embedding for dynamic networks. However, they either rely on knowledge of vertex attributes, suffer high-time complexity or need to be re-trained without closed-form expression. Thus the approach of adapting the existing methods to the streaming environment faces non-trivial technical challenges. These challenges motivate developing new approaches to the problems of streaming network embedding. In this paper, We propose a new framework that is able to generate latent features for new vertices with high efficiency and low complexity under specified iteration rounds. We formulate a constrained optimization problem for the modification of the representation resulting from a stream arrival. We show this problem has no closed-form solution and instead develop an online approximation solution. Our solution follows three steps: (1) identify vertices affected by new vertices, (2) generate latent features for new vertices, and (3) update the latent features of the most affected vertices. The generated representations are provably feasible and not far from the optimal ones in terms of expectation. Multi-class classification and clustering on five real-world networks demonstrate that our model can efficiently update vertex representations and simultaneously achieve comparable or even better performance.

Heteroscedastic Bandits with Reneging

Although shown to be useful in many areas as models for solving sequential decision problems with side observations (contexts), contextual bandits are subject to two major limitations. First, they neglect user "reneging" that occurs in real-world applications. That is, users unsatisfied with an interaction quit future interactions forever. Second, they assume that the reward distribution is homoscedastic, which is often invalidated by real-world datasets, e.g., datasets from finance. We propose a novel model of "heteroscedastic contextual bandits with reneging" to overcome the two limitations. Our model allows each user to have a distinct "acceptance level," with any interaction falling short of that level resulting in that user reneging. It also allows the variance to be a function of context. We develop a UCB-type of policy, called HR-UCB, and prove that with high probability it achieves $\mathcal{O}\Big(\sqrt{{T}}\big(\log({T})\big)^{3/2}\Big)$ regret.