Related papers: A unified worst case for classical simplex and pol…

Kitahara and Mizuno (2010) get two upper bounds for the number of different basic feasible solutions generated by Dantzig's simplex method. The size of the bounds highly depends on the ratio between the maximum and minimum values of all the…

Linear programming has been practically solved mainly by simplex and interior point methods. Compared with the weakly polynomial complexity obtained by the interior point methods, the existence of strongly polynomial bounds for the length…

We present new pivot rules for the Simplex method for LPs over 0/1 polytopes. We show that the number of non-degenerate steps taken using these rules is strongly polynomial and even linear in the dimension or in the number of variables. Our…

We study the policy testing problem in discounted Markov decision processes (MDPs) in the fixed-confidence setting under a generative model with static sampling. The goal is to decide whether the value of a given policy exceeds a specified…

A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in…

We prove new upper and lower bounds for sample complexity of finding an $\epsilon$-optimal policy of an infinite-horizon average-reward Markov decision process (MDP) given access to a generative model. When the mixing time of the…

We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…

In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…

We consider reinforcement learning in changing Markov Decision Processes where both the state-transition probabilities and the reward functions may vary over time. For this problem setting, we propose an algorithm using a sliding window…

We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space $|\mathcal{S}|$ and a finite action space $|\mathcal{A}|$. We show that any randomized algorithm needs a…

Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence…

In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…

Policy optimization algorithms are crucial in many fields but challenging to grasp and implement, often due to complex calculations related to Markov decision processes and varying use of discount and average reward setups. This paper…

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$…

Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the…

We propose a new policy, called the LP-update policy, to solve finite horizon weakly-coupled Markov decision processes. The latter can be seen as multi-constraint multi-action bandits, and generalize the classical restless bandit problems.…

Motivated from Bertsekas' recent study on policy iteration (PI) for solving the problems of infinite-horizon discounted Markov decision processes (MDPs) in an on-line setting, we develop an off-line PI integrated with a multi-policy…

We introduce a contractive abstract dynamic programming framework and related policy iteration algorithms, specifically designed for sequential zero-sum games and minimax problems with a general structure. Aside from greater generality, the…

Many interventions, such as vaccines in clinical trials or coupons in online marketplaces, must be assigned sequentially without full knowledge of their effects. Multi-armed bandit algorithms have proven successful in such settings.…

Dynamic Programming (DP) provides standard algorithms to solve Markov Decision Processes. However, these algorithms generally do not optimize a scalar objective function. In this paper, we draw connections between DP and (constrained)…