Structured Policy Iteration for Linear Quadratic Regulator

Linear quadratic regulator (LQR) is one of the most popular frameworks to tackle continuous Markov decision process tasks. With its fundamental theory and tractable optimal policy, LQR has been revisited and analyzed in recent years, in terms of reinforcement learning scenarios such as the model-free or model-based setting. In this paper, we introduce the \textit{Structured Policy Iteration} (S-PI) for LQR, a method capable of deriving a structured linear policy. Such a structured policy with (block) sparsity or low-rank can have significant advantages over the standard LQR policy: more interpretable, memory-efficient, and well-suited for the distributed setting. In order to derive such a policy, we first cast a regularized LQR problem when the model is known. Then, our Structured Policy Iteration (S-PI) algorithm, which takes a policy evaluation step and a policy improvement step in an iterative manner, can solve this regularized LQR efficiently. We further extend the S-PI algorithm to the model-free setting where a smoothing procedure is adopted to estimate the gradient. In both the known-model and model-free setting, we prove convergence analysis under the proper choice of parameters. Finally, the experiments demonstrate the advantages of S-PI in terms of balancing the LQR performance and level of structure by varying the weight parameter.

Influence Diagram Bandits: Variational Thompson Sampling for Structured Bandit Problems

We propose a novel framework for structured bandits, which we call an influence diagram bandit. Our framework captures complex statistical dependencies between actions, latent variables, and observations; and thus unifies and extends many existing models, such as combinatorial semi-bandits, cascading bandits, and low-rank bandits. We develop novel online learning algorithms that learn to act efficiently in our models. The key idea is to track a structured posterior distribution of model parameters, either exactly or approximately. To act, we sample model parameters from their posterior and then use the structure of the influence diagram to find the most optimistic action under the sampled parameters. We empirically evaluate our algorithms in three structured bandit problems, and show that they perform as well as or better than problem-specific state-of-the-art baselines.

Hypermodels for Exploration

We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its size, and as such, prior work has typically been limited to ensembles with tens of elements. We show that alternative hypermodels can enjoy dramatic efficiency gains, enabling behavior that would otherwise require hundreds or thousands of elements, and even succeed in situations where ensemble methods fail to learn regardless of size. This allows more accurate approximation of Thompson sampling as well as use of more sophisticated exploration schemes. In particular, we consider an approximate form of information-directed sampling and demonstrate performance gains relative to Thompson sampling. As alternatives to ensembles, we consider linear and neural network hypermodels, also known as hypernetworks. We prove that, with neural network base models, a linear hypermodel can represent essentially any distribution over functions, and as such, hypernetworks are no more expressive.

Improving Adversarial Text Generation by Modeling the Distant Future

Auto-regressive text generation models usually focus on local fluency, and may cause inconsistent semantic meaning in long text generation. Further, automatically generating words with similar semantics is challenging, and hand-crafted linguistic rules are difficult to apply. We consider a text planning scheme and present a model-based imitation-learning approach to alleviate the aforementioned issues. Specifically, we propose a novel guider network to focus on the generative process over a longer horizon, which can assist next-word prediction and provide intermediate rewards for generator optimization. Extensive experiments demonstrate that the proposed method leads to improved performance.

Nested-Wasserstein Self-Imitation Learning for Sequence Generation

Reinforcement learning (RL) has been widely studied for improving sequence-generation models. However, the conventional rewards used for RL training typically cannot capture sufficient semantic information and therefore render model bias. Further, the sparse and delayed rewards make RL exploration inefficient. To alleviate these issues, we propose the concept of nested-Wasserstein distance for distributional semantic matching. To further exploit it, a novel nested-Wasserstein self-imitation learning framework is developed, encouraging the model to exploit historical high-rewarded sequences for enhanced exploration and better semantic matching. Our solution can be understood as approximately executing proximal policy optimization with Wasserstein trust-regions. Experiments on a variety of unconditional and conditional sequence-generation tasks demonstrate the proposed approach consistently leads to improved performance.

Bootstrapping Upper Confidence Bound

Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration inequalities, which thus lead to over-exploration. In this paper, we propose a non-parametric and data-dependent UCB algorithm based on the multiplier bootstrap. To improve its finite sample performance, we further incorporate second-order correction into the above construction. In theory, we derive both problem-dependent and problem-independent regret bounds for multi-armed bandits under a much weaker tail assumption than the standard sub-Gaussianity. Numerical results demonstrate significant regret reductions by our method, in comparison with several baselines in a range of multi-armed and linear bandit problems.

Waterfall Bandits: Learning to Sell Ads Online

A popular approach to selling online advertising is by a waterfall, where a publisher makes sequential price offers to ad networks for an inventory, and chooses the winner in that order. The publisher picks the order and prices to maximize her revenue. A traditional solution is to learn the demand model and then subsequently solve the optimization problem for the given demand model. This will incur a linear regret. We design an online learning algorithm for solving this problem, which interleaves learning and optimization, and prove that this algorithm has sublinear regret. We evaluate the algorithm on both synthetic and real-world data, and show that it quickly learns high quality pricing strategies. This is the first principled study of learning a waterfall design online by sequential experimentation.

Stochastic Online Learning with Probabilistic Graph Feedback

We consider a problem of stochastic online learning with general probabilistic graph feedback. Two cases are covered. (a) The one-step case where for each edge $(i,j)$ with probability $p_{ij}$ in the probabilistic feedback graph. After playing arm $i$ the learner observes a sample reward feedback of arm $j$ with independent probability $p_{ij}$. (b) The cascade case where after playing arm $i$ the learner observes feedback of all arms $j$ in a probabilistic cascade starting from $i$ -- for each $(i,j)$ with probability $p_{ij}$, if arm $i$ is played or observed, then a reward sample of arm $j$ would be observed with independent probability $p_{ij}$. Previous works mainly focus on deterministic graphs which corresponds to one-step case with $p_{ij} \in \{0,1\}$, an adversarial sequence of graphs with certain topology guarantees or a specific type of random graphs. We analyze the asymptotic lower bounds and design algorithms in both cases. The regret upper bounds of the algorithms match the lower bounds with high probability.

Scalable Thompson Sampling via Optimal Transport

Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest models. Consequently, efficient computation of an approximate posterior distribution is a crucial problem for scalable TS with complex models, such as neural networks. In this paper, we use distribution optimization techniques to approximate the posterior distribution, solved via Wasserstein gradient flows. Based on the framework, a principled particle-optimization algorithm is developed for TS to approximate the posterior efficiently. Our approach is scalable and does not make explicit distribution assumptions on posterior approximations. Extensive experiments on both synthetic data and real large-scale data demonstrate the superior performance of the proposed methods.