We consider reinforcement learning (RL) in Markov Decision Processes in which an agent repeatedly interacts with an environment that is modeled by a controlled Markov process. At each time step $t$, it earns a reward, and also incurs a cost-vector consisting of $M$ costs. We design learning algorithms that maximize the cumulative reward earned over a time horizon of $T$ time-steps, while simultaneously ensuring that the average values of the $M$ cost expenditures are bounded by agent-specified thresholds $c^{ub}_i,i=1,2,\ldots,M$. The considerations on the cumulative cost expenditures departs from the existing literature, in that the agent now additionally needs to balance the cost expenses in an online manner, while simultaneously performing the exploration-exploitation trade-off that is typically encountered in RL tasks. In order to measure the performance of a reinforcement learning algorithm that satisfies the average cost constraints, we define an $M+1$ dimensional regret vector that is composed of its reward regret, and $M$ cost regrets. The reward regret measures the sub-optimality in the cumulative reward, while the $i$-th component of the cost regret vector is the difference between its $i$-th cumulative cost expense and the expected cost expenditures $Tc^{ub}_i$. We prove that with a high probablity, the regret vector of UCRL-CMDP is upper-bounded as $O\left( S\sqrt{AT^{1.5}\log(T)}\right)$, where $S$ is the number of states, $A$ is the number of actions, and $T$ is the time horizon. We further show how to reduce the regret of a desired subset of the $M$ costs, at the expense of increasing the regrets of rewards and the remaining costs. To the best of our knowledge, ours is the only work that considers non-episodic RL under average cost constraints, and derive algorithms that can~\emph{tune the regret vector} according to the agent's requirements on its cost regrets.
相關內容
Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are not violated. In this paper, we propose Safe-CDDP, a safe trajectory optimization and control approach for systems under additive uncertainties and non-linear safety constraints based on constrained differential dynamic programming (DDP). The safety of the robot during its motion is formulated as chance constraints with user-chosen probabilities of constraint satisfaction. The chance constraints are transformed into deterministic ones in DDP formulation by constraint tightening. To avoid over-conservatism during constraint tightening, linear control gains of the feedback policy derived from the constrained DDP are used in the approximation of closed-loop uncertainty propagation in prediction. The proposed algorithm is empirically evaluated on three different robot dynamics with up to 12 degrees of freedom in simulation. The computational feasibility and applicability of the approach are demonstrated with a physical hardware implementation.
We study constrained reinforcement learning (CRL) from a novel perspective by setting constraints directly on state density functions, rather than the value functions considered by previous works. State density has a clear physical and mathematical interpretation, and is able to express a wide variety of constraints such as resource limits and safety requirements. Density constraints can also avoid the time-consuming process of designing and tuning cost functions required by value function-based constraints to encode system specifications. We leverage the duality between density functions and Q functions to develop an effective algorithm to solve the density constrained RL problem optimally and the constrains are guaranteed to be satisfied. We prove that the proposed algorithm converges to a near-optimal solution with a bounded error even when the policy update is imperfect. We use a set of comprehensive experiments to demonstrate the advantages of our approach over state-of-the-art CRL methods, with a wide range of density constrained tasks as well as standard CRL benchmarks such as Safety-Gym.
In real world settings, numerous constraints are present which are hard to specify mathematically. However, for the real world deployment of reinforcement learning (RL), it is critical that RL agents are aware of these constraints, so that they can act safely. In this work, we consider the problem of learning constraints from demonstrations of a constraint-abiding agent's behavior. We experimentally validate our approach and show that our framework can successfully learn the most likely constraints that the agent respects. We further show that these learned constraints are \textit{transferable} to new agents that may have different morphologies and/or reward functions. Previous works in this regard have either mainly been restricted to tabular (discrete) settings, specific types of constraints or assume the environment's transition dynamics. In contrast, our framework is able to learn arbitrary \textit{Markovian} constraints in high-dimensions in a completely model-free setting. The code can be found it: \url{//github.com/shehryar-malik/icrl}.
We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to guarantee both optimism and convergence of the associated value iteration scheme. We prove that EB-SSP achieves the minimax regret rate $\widetilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the number of episodes, $S$ is the number of states, $A$ is the number of actions and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of $B_{\star}$, nor of $T_{\star}$ which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of $T_{\star}$ is available) where the regret only contains a logarithmic dependence on $T_{\star}$, thus yielding the first horizon-free regret bound beyond the finite-horizon MDP setting.
Methods proposed in the literature towards continual deep learning typically operate in a task-based sequential learning setup. A sequence of tasks is learned, one at a time, with all data of current task available but not of previous or future tasks. Task boundaries and identities are known at all times. This setup, however, is rarely encountered in practical applications. Therefore we investigate how to transform continual learning to an online setup. We develop a system that keeps on learning over time in a streaming fashion, with data distributions gradually changing and without the notion of separate tasks. To this end, we build on the work on Memory Aware Synapses, and show how this method can be made online by providing a protocol to decide i) when to update the importance weights, ii) which data to use to update them, and iii) how to accumulate the importance weights at each update step. Experimental results show the validity of the approach in the context of two applications: (self-)supervised learning of a face recognition model by watching soap series and learning a robot to avoid collisions.
We consider the exploration-exploitation trade-off in reinforcement learning and we show that an agent imbued with a risk-seeking utility function is able to explore efficiently, as measured by regret. The parameter that controls how risk-seeking the agent is can be optimized exactly, or annealed according to a schedule. We call the resulting algorithm K-learning and show that the corresponding K-values are optimistic for the expected Q-values at each state-action pair. The K-values induce a natural Boltzmann exploration policy for which the `temperature' parameter is equal to the risk-seeking parameter. This policy achieves an expected regret bound of $\tilde O(L^{3/2} \sqrt{S A T})$, where $L$ is the time horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the total number of elapsed time-steps. This bound is only a factor of $L$ larger than the established lower bound. K-learning can be interpreted as mirror descent in the policy space, and it is similar to other well-known methods in the literature, including Q-learning, soft-Q-learning, and maximum entropy policy gradient, and is closely related to optimism and count based exploration methods. K-learning is simple to implement, as it only requires adding a bonus to the reward at each state-action and then solving a Bellman equation. We conclude with a numerical example demonstrating that K-learning is competitive with other state-of-the-art algorithms in practice.
Embedding models for entities and relations are extremely useful for recovering missing facts in a knowledge base. Intuitively, a relation can be modeled by a matrix mapping entity vectors. However, relations reside on low dimension sub-manifolds in the parameter space of arbitrary matrices---for one reason, composition of two relations $\boldsymbol{M}_1,\boldsymbol{M}_2$ may match a third $\boldsymbol{M}_3$ (e.g. composition of relations currency_of_country and country_of_film usually matches currency_of_film_budget), which imposes compositional constraints to be satisfied by the parameters (i.e. $\boldsymbol{M}_1\cdot \boldsymbol{M}_2\approx \boldsymbol{M}_3$). In this paper we investigate a dimension reduction technique by training relations jointly with an autoencoder, which is expected to better capture compositional constraints. We achieve state-of-the-art on Knowledge Base Completion tasks with strongly improved Mean Rank, and show that joint training with an autoencoder leads to interpretable sparse codings of relations, helps discovering compositional constraints and benefits from compositional training. Our source code is released at github.com/tianran/glimvec.
Inferring other agents' mental states such as their knowledge, beliefs and intentions is thought to be essential for effective interactions with other agents. Recently, multiagent systems trained via deep reinforcement learning have been shown to succeed in solving different tasks, but it remains unclear how each agent modeled or represented other agents in their environment. In this work we test whether deep reinforcement learning agents explicitly represent other agents' intentions (their specific aims or goals) during a task in which the agents had to coordinate the covering of different spots in a 2D environment. In particular, we tracked over time the performance of a linear decoder trained to predict the final goal of all agents from the hidden state of each agent's neural network controller. We observed that the hidden layers of agents represented explicit information about other agents' goals, i.e. the target landmark they ended up covering. We also performed a series of experiments, in which some agents were replaced by others with fixed goals, to test the level of generalization of the trained agents. We noticed that during the training phase the agents developed a differential preference for each goal, which hindered generalization. To alleviate the above problem, we propose simple changes to the MADDPG training algorithm which leads to better generalization against unseen agents. We believe that training protocols promoting more active intention reading mechanisms, e.g. by preventing simple symmetry-breaking solutions, is a promising direction towards achieving a more robust generalization in different cooperative and competitive tasks.
Existing visual tracking methods usually localize a target object with a bounding box, in which the performance of the foreground object trackers or detectors is often affected by the inclusion of background clutter. To handle this problem, we learn a patch-based graph representation for visual tracking. The tracked object is modeled by with a graph by taking a set of non-overlapping image patches as nodes, in which the weight of each node indicates how likely it belongs to the foreground and edges are weighted for indicating the appearance compatibility of two neighboring nodes. This graph is dynamically learned and applied in object tracking and model updating. During the tracking process, the proposed algorithm performs three main steps in each frame. First, the graph is initialized by assigning binary weights of some image patches to indicate the object and background patches according to the predicted bounding box. Second, the graph is optimized to refine the patch weights by using a novel alternating direction method of multipliers. Third, the object feature representation is updated by imposing the weights of patches on the extracted image features. The object location is predicted by maximizing the classification score in the structured support vector machine. Extensive experiments show that the proposed tracking algorithm performs well against the state-of-the-art methods on large-scale benchmark datasets.
This paper proposes a Reinforcement Learning (RL) algorithm to synthesize policies for a Markov Decision Process (MDP), such that a linear time property is satisfied. We convert the property into a Limit Deterministic Buchi Automaton (LDBA), then construct a product MDP between the automaton and the original MDP. A reward function is then assigned to the states of the product automaton, according to accepting conditions of the LDBA. With this reward function, our algorithm synthesizes a policy that satisfies the linear time property: as such, the policy synthesis procedure is "constrained" by the given specification. Additionally, we show that the RL procedure sets up an online value iteration method to calculate the maximum probability of satisfying the given property, at any given state of the MDP - a convergence proof for the procedure is provided. Finally, the performance of the algorithm is evaluated via a set of numerical examples. We observe an improvement of one order of magnitude in the number of iterations required for the synthesis compared to existing approaches.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191