arXiv subjects

Alihan Hüyük

Publications and source records attributed to Alihan Hüyük.

22 records · Page 2Linked to original sources

arXiv2021

Learning "What-if" Explanations for Sequential Decision-Making

Building interpretable parameterizations of real-world decision-making on the basis of demonstrated behavior -- i.e. trajectories of observations and actions made by an expert maximizing some unknown reward function -- is essential for introspecting and auditing policies in different institutions. In this paper, we propose learning explanations of expert decisions by modeling their reward function in terms of preferences with respect to "what if" outcomes: Given the current history of observations, what would happen if we took a particular action? To learn these cost-benefit tradeoffs associated with the expert's actions, we integrate counterfactual reasoning into batch inverse reinforcement learning. This offers a principled way of defining reward functions and explaining expert behavior, and also satisfies the constraints of real-world decision-making -- where active experimentation is often impossible (e.g. in healthcare). Additionally, by estimating the effects of different actions, counterfactuals readily tackle the off-policy nature of policy evaluation in the batch setting, and can naturally accommodate settings where the expert policies depend on histories of observations rather than just current states. Through illustrative experiments in both real and simulated medical environments, we highlight the effectiveness of our batch, counterfactual inverse reinforcement learning approach in recovering accurate and interpretable descriptions of behavior.

cs.LG↗

arXiv2020

Thompson Sampling for Combinatorial Network Optimization in Unknown Environments

Influence maximization, adaptive routing, and dynamic spectrum allocation all require choosing the right action from a large set of alternatives. Thanks to the advances in combinatorial optimization, these and many similar problems can be efficiently solved given an environment with known stochasticity. In this paper, we take this one step further and focus on combinatorial optimization in unknown environments. We consider a very general learning framework called combinatorial multi-armed bandit with probabilistically triggered arms and a very powerful Bayesian algorithm called Combinatorial Thompson Sampling (CTS). Under the semi-bandit feedback model and assuming access to an oracle without knowing the expected base arm outcomes beforehand, we show that when the expected reward is Lipschitz continuous in the expected base arm outcomes CTS achieves $O(\sum_{i =1}^m\log T/(p_iΔ_i))$ regret and $O(\max\{\mathbb{E}[m\sqrt{T\log T/p^*}],\mathbb{E}[m^2/p^*]\})$ Bayesian regret, where $m$ denotes the number of base arms, $p_i$ and $Δ_i$ denote the minimum non-zero triggering probability and the minimum suboptimality gap of base arm $i$ respectively, $T$ denotes the time horizon, and $p^*$ denotes the overall minimum non-zero triggering probability. We also show that when the expected reward satisfies the triggering probability modulated Lipschitz continuity, CTS achieves $O(\max\{m\sqrt{T\log T},m^2\})$ Bayesian regret, and when triggering probabilities are non-zero for all base arms, CTS achieves $O(1/p^*\log(1/p^*))$ regret independent of the time horizon. Finally, we numerically compare CTS with algorithms based on upper confidence bounds in several networking problems and show that CTS outperforms these algorithms by at least an order of magnitude in majority of the cases.

cs.LG↗

arXiv2019

Lexicographic Multiarmed Bandit

We consider a multiobjective multiarmed bandit problem with lexicographically ordered objectives. In this problem, the goal of the learner is to select arms that are lexicographic optimal as much as possible without knowing the arm reward distributions beforehand. We capture this goal by defining a multidimensional form of regret that measures the loss of the learner due to not selecting lexicographic optimal arms, and then, consider two settings where the learner has prior information on the expected arm rewards. In the first setting, the learner only knows for each objective the lexicographic optimal expected reward. In the second setting, it only knows for each objective near-lexicographic optimal expected rewards. For both settings we prove that the learner achieves expected regret uniformly bounded in time. The algorithm we propose for the second setting also attains bounded regret for the multiarmed bandit with satisficing objectives. In addition, we also consider the harder prior-free case, and show that the learner can still achieve sublinear in time gap-free regret. Finally, we experimentally evaluate performance of the proposed algorithms in a variety of multiobjective learning problems.

cs.LG↗

arXiv2019

Analysis of Thompson Sampling for Combinatorial Multi-armed Bandit with Probabilistically Triggered Arms

We analyze the regret of combinatorial Thompson sampling (CTS) for the combinatorial multi-armed bandit with probabilistically triggered arms under the semi-bandit feedback setting. We assume that the learner has access to an exact optimization oracle but does not know the expected base arm outcomes beforehand. When the expected reward function is Lipschitz continuous in the expected base arm outcomes, we derive $O(\sum_{i =1}^m \log T / (p_i Δ_i))$ regret bound for CTS, where $m$ denotes the number of base arms, $p_i$ denotes the minimum non-zero triggering probability of base arm $i$ and $Δ_i$ denotes the minimum suboptimality gap of base arm $i$. We also compare CTS with combinatorial upper confidence bound (CUCB) via numerical experiments on a cascading bandit problem.

cs.LG↗