to

### Constrained Upper Confidence Reinforcement Learning

Constrained Markov Decision Processes are a class of stochastic decision problems in which the decision maker must select a policy that satisfies auxiliary cost constraints. This paper extends upper confidence reinforcement learning for settings in which the reward function and the constraints, described by cost functions, are unknown a priori but the transition kernel is known. Such a setting is well-motivated by a number of applications including exploration of unknown, potentially unsafe, environments. We present an algorithm C-UCRL and show that it achieves sub-linear regret ($O(T^{\frac{3}{4}}\sqrt{\log(T/\delta)})$) with respect to the reward while satisfying the constraints even while learning with probability $1-\delta$. Illustrative examples are provided.

### Data-efficient Hindsight Off-policy Option Learning

Solutions to most complex tasks can be decomposed into simpler, intermediate skills, reusable across wider ranges of problems. We follow this concept and introduce Hindsight Off-policy Options (HO2), a new algorithm for efficient and robust option learning. The algorithm relies on critic-weighted maximum likelihood estimation and an efficient dynamic programming inference procedure over off-policy trajectories. We can backpropagate through the inference procedure through time and the policy components for every time-step, making it possible to train all component's parameters off-policy, independently of the data-generating behavior policy. Experimentally, we demonstrate that HO2 outperforms competitive baselines and solves demanding robot stacking and ball-in-cup tasks from raw pixel inputs in simulation. We further compare autoregressive option policies with simple mixture policies, providing insights into the relative impact of two types of abstractions common in the options framework: action abstraction and temporal abstraction. Finally, we illustrate challenges caused by stale data in off-policy options learning and provide effective solutions.

### Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning

Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, observed actions are often confounded with transitions by unobserved variables, rendering exact evaluation of new policies impossible, i.e., unidentifiable. We develop a robust approach that estimates sharp bounds on the (unidentifiable) value of a given policy in an infinite-horizon problem given data from another policy with unobserved confounding subject to a sensitivity model. We phrase the problem precisely as computing the support function of the set of all stationary state-occupancy ratios that agree with both the data and the sensitivity model. We show how to express this set using a new partially identified estimating equation and prove convergence to the sharp bounds, as we collect more confounded data. We prove that membership in the set can be checked by solving a linear program, while the support function is given by a difficult nonconvex optimization problem. We leverage an analytical solution for the finite-state-space case to develop approximations based on nonconvex projected gradient descent. We demonstrate the resulting bounds empirically.

### Lyapunov Barrier Policy Optimization

Deploying Reinforcement Learning (RL) agents in the real-world require that the agents satisfy safety constraints. Current RL agents explore the environment without considering these constraints, which can lead to damage to the hardware or even other agents in the environment. We propose a new method, LBPO, that uses a Lyapunov-based barrier function to restrict the policy update to a safe set for each training iteration. Our method also allows the user to control the conservativeness of the agent with respect to the constraints in the environment. LBPO significantly outperforms state-of-the-art baselines in terms of the number of constraint violations during training while being competitive in terms of performance. Further, our analysis reveals that baselines like CPO and SDDPG rely mostly on backtracking to ensure safety rather than safe projection, which provides insight into why previous methods might not have effectively limit the number of constraint violations.

### Deep imagination is a close to optimal policy for planning in large decision trees under limited resources

Many decisions involve choosing an uncertain course of actions in deep and wide decision trees, as when we plan to visit an exotic country for vacation. In these cases, exhaustive search for the best sequence of actions is not tractable due to the large number of possibilities and limited time or computational resources available to make the decision. Therefore, planning agents need to balance breadth (exploring many actions at each level of the tree) and depth (exploring many levels in the tree) to allocate optimally their finite search capacity. We provide efficient analytical solutions and numerical analysis to the problem of allocating finite sampling capacity in one shot to large decision trees. We find that in general the optimal policy is to allocate few samples per level so that deep levels can be reached, thus favoring depth over breadth search. In contrast, in poor environments and at low capacity, it is best to broadly sample branches at the cost of not sampling deeply, although this policy is marginally better than deep allocations. Our results provide a theoretical foundation for the optimality of deep imagination for planning and show that it is a generally valid heuristic that could have evolved from the finite constraints of cognitive systems.