Vincent Leon

Vincent Leon, S. Rasoul Etesami

We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and minimize their regret over a finite time horizon through interacting with the environment. We devise a simple and efficient model-based algorithm that achieves $\widetilde{O}(LX\sqrt{TA})$ regret with high probability, where $L$ is the episode length, $T$ is the number of episodes, and $X$ and $A$ are the cardinalities of the state space and the action space, respectively. The proposed algorithm, which is based on the concept of ``optimism in the face of uncertainty", maintains confidence sets of transition and reward functions and uses occupancy measures to connect the online MDP with linear programming. It achieves a tighter regret bound compared to the existing works that use a similar confidence set framework and improves computational effort compared to those that use a different framework but with a slightly tighter regret bound.

Vincent Leon, S. Rasoul Etesami

We consider the problem of online dynamic mechanism design for sequential auctions in unknown environments, where the underlying market and, thus, the bidders' values vary over time as interactions between the seller and the bidders progress. We model the sequential auctions as an infinite-horizon average-reward Markov decision process (MDP). In each round, the seller determines an allocation and sets a payment for each bidder, while each bidder receives a private reward and submits a sealed bid to the seller. The state, which represents the underlying market, evolves according to an unknown transition kernel and the seller's allocation policy without episodic resets. We first extend the Vickrey-Clarke-Groves (VCG) mechanism to sequential auctions, thereby obtaining a dynamic counterpart that preserves the desired properties: efficiency, truthfulness, and individual rationality. We then focus on the online setting and develop a reinforcement learning algorithm for the seller to learn the underlying MDP and implement a mechanism that closely resembles the dynamic VCG mechanism. We show that the learned mechanism approximately satisfies efficiency, truthfulness, and individual rationality and achieves guaranteed performance in terms of various notions of regret.

Vincent Leon, S. Rasoul Etesami

In this paper, we study the strategic allocation of limited resources using a Colonel Blotto game (CBG) under a dynamic setting and analyze the problem using an online learning approach. In this model, one of the players is a learner who has limited troops to allocate over a finite time horizon, and the other player is an adversary. In each round, the learner plays a one-shot Colonel Blotto game with the adversary and strategically determines the allocation of troops among battlefields based on past observations. The adversary chooses its allocation action randomly from some fixed distribution that is unknown to the learner. The learner's objective is to minimize its regret, which is the difference between the cumulative reward of the best mixed strategy and the realized cumulative reward by following a learning algorithm while not violating the budget constraint. The learning in dynamic CBG is analyzed under the framework of combinatorial bandits and bandits with knapsacks. We first convert the budget-constrained dynamic CBG to a path planning problem on a directed graph. We then devise an efficient algorithm that combines a special combinatorial bandit algorithm for path planning problem and a bandits with knapsack algorithm to cope with the budget constraint. The theoretical analysis shows that the learner's regret is bounded by a term sublinear in time horizon and polynomial in other parameters. Finally, we justify our theoretical results by carrying out simulations for various scenarios.

S. Rasoul Etesami, Negar Kiyavash, Vincent Leon et al.

We consider a learning system based on the conventional multiplicative weight (MW) rule that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the system. The loss of the system is naturally defined to be the aggregate absolute difference between the sequence of predicted outcomes and the true outcomes. We consider this problem under both offline and online settings. In the offline setting where the malicious expert must choose its entire sequence of decisions a priori, we show somewhat surprisingly that a simple greedy policy of always reporting false prediction is asymptotically optimal with an approximation ratio of $1+O(\sqrt{\frac{\ln N}{N}})$, where $N$ is the total number of prediction stages. In particular, we describe a policy that closely resembles the structure of the optimal offline policy. For the online setting where the malicious expert can adaptively make its decisions, we show that the optimal online policy can be efficiently computed by solving a dynamic program in $O(N^3)$. Our results provide a new direction for vulnerability assessment of commonly used learning algorithms to adversarial attacks where the threat is an integral part of the system.