Min Wen

Min Wen, Ufuk Topcu

Stochastic games are often used to model reactive processes. We consider the problem of synthesizing an optimal almost-sure winning strategy in a two-player (namely a system and its environment) turn-based stochastic game with both a qualitative objective as a Rabin winning condition, and a quantitative objective as a discounted reward. Optimality is considered only over the almost-sure winning strategies, i.e., system strategies that guarantee the satisfaction of the Rabin condition with probability 1 regardless of the environment's strategy. We show that optimal almost-sure winning strategies may need infinite memory, but epsilon-optimal almost-sure winning strategies can always be finite-memory or even memoryless. We identify a sufficient and necessary condition of the existence of memoryless epsilon-optimal almost-sure winning strategies and propose an algorithm to compute one when this condition is satisfied.

Min Wen, Chengchang Liu, Ahmed Abdelmoniem et al.

Bilevel optimization, crucial for hyperparameter tuning, meta-learning and reinforcement learning, remains less explored in the decentralized learning paradigm, such as decentralized federated learning (DFL). Typically, decentralized bilevel methods rely on both gradients and Hessian matrices to approximate hypergradients of upper-level models. However, acquiring and sharing the second-order oracle is compute and communication intensive. % and sharing this information incurs heavy communication overhead. To overcome these challenges, this paper introduces a fully first-order decentralized method for decentralized Bilevel optimization, $\text{C}^2$DFB which is both compute- and communicate-efficient. In $\text{C}^2$DFB, each learning node optimizes a min-min-max problem to approximate hypergradient by exclusively using gradients information. To reduce the traffic load at the inner-loop of solving the lower-level problem, $\text{C}^2$DFB incorporates a lightweight communication protocol for efficiently transmitting compressed residuals of local parameters. % during the inner loops. Rigorous theoretical analysis ensures its convergence % of the algorithm, indicating a first-order oracle calls of $\tilde{\mathcal{O}}(ε^{-4})$. Experiments on hyperparameter tuning and hyper-representation tasks validate the superiority of $\text{C}^2$DFB across various typologies and heterogeneous data distributions.

Farzan Memarian, Zhe Xu, Bo Wu et al.

We consider the problem of reward learning for temporally extended tasks. For reward learning, inverse reinforcement learning (IRL) is a widely used paradigm. Given a Markov decision process (MDP) and a set of demonstrations for a task, IRL learns a reward function that assigns a real-valued reward to each state of the MDP. However, for temporally extended tasks, the underlying reward function may not be expressible as a function of individual states of the MDP. Instead, the history of visited states may need to be considered to determine the reward at the current state. To address this issue, we propose an iterative algorithm to learn a reward function for temporally extended tasks. At each iteration, the algorithm alternates between two modules, a task inference module that infers the underlying task structure and a reward learning module that uses the inferred task structure to learn a reward function. The task inference module produces a series of queries, where each query is a sequence of subgoals. The demonstrator provides a binary response to each query by attempting to execute it in the environment and observing the environment's feedback. After the queries are answered, the task inference module returns an automaton encoding its current hypothesis of the task structure. The reward learning module augments the state space of the MDP with the states of the automaton. The module then proceeds to learn a reward function over the augmented state space using a novel deep maximum entropy IRL algorithm. This iterative process continues until it learns a reward function with satisfactory performance. The experiments show that the proposed algorithm significantly outperforms several IRL baselines on temporally extended tasks.

Min Wen, Osbert Bastani, Ufuk Topcu

It has recently been shown that if feedback effects of decisions are ignored, then imposing fairness constraints such as demographic parity or equality of opportunity can actually exacerbate unfairness. We propose to address this challenge by modeling feedback effects as Markov decision processes (MDPs). First, we propose analogs of fairness properties for the MDP setting. Second, we propose algorithms for learning fair decision-making policies for MDPs. Finally, we demonstrate the need to account for dynamical effects using simulations on a loan applicant MDP.

Michael L. Littman, Ufuk Topcu, Jie Fu et al.

We propose a new task-specification language for Markov decision processes that is designed to be an improvement over reward functions by being environment independent. The language is a variant of Linear Temporal Logic (LTL) that is extended to probabilistic specifications in a way that permits approximations to be learned in finite time. We provide several small environments that demonstrate the advantages of our geometric LTL (GLTL) language and illustrate how it can be used to specify standard reinforcement-learning tasks straightforwardly.

Min Wen, Ruediger Ehlers, Ufuk Topcu

We consider a problem on the synthesis of reactive controllers that optimize some a priori unknown performance criterion while interacting with an uncontrolled environment such that the system satisfies a given temporal logic specification. We decouple the problem into two subproblems. First, we extract a (maximally) permissive strategy for the system, which encodes multiple (possibly all) ways in which the system can react to the adversarial environment and satisfy the specifications. Then, we quantify the a priori unknown performance criterion as a (still unknown) reward function and compute an optimal strategy for the system within the operating envelope allowed by the permissive strategy by using the so-called maximin-Q learning algorithm. We establish both correctness (with respect to the temporal logic specifications) and optimality (with respect to the a priori unknown performance criterion) of this two-step technique for a fragment of temporal logic specifications. For specifications beyond this fragment, correctness can still be preserved, but the learned strategy may be sub-optimal. We present an algorithm to the overall problem, and demonstrate its use and computational requirements on a set of robot motion planning examples.