We simplify the network cost problem by assuming that all network connections have equal latency. The loads have an entry point at some host or hosts in system; a load is routed from an entry point to a host that handles the load, constrained by the network topology of the system, which may contain cycles. In our experiments, we define two different cost models for CRL that only differ by their cost models: in the discrete cost model , a successful store action for a load has no cost and an unsuccessful store action has some fixed high cost; in the gradient cost model, a successful store action has a cost that is a function of the spare capacity at the agent and an unsuccessful store action has some fixed high cost.

In both models, we assigned a fixed connection cost for forwarding a load to a neighboring agent in a real network, the connection cost could be measured from the underlying network message sending cost. The purpose of these two different CRL models is to show how the algorithm can be tuned exploit the first available space at agents discrete model will prefer the first agent with spare capacity , or to exploit space at higher capacity agents gradient cost model will prefer agents with higher spare capacity.

We ran our experiments in a discrete event simulator written in Java.

The experiments define a topology of agents with connections between them, and a set of DOPs, where each DOP is a load storage problem. The unit of time in the experiments corresponds to a step in the simulator, where a step involves the execution of an action storage, delegation or discovery by an agent. The goal of this experiment is to evaluate whether agents can exploit their total load capacity maximize resource usage , and minimize the amount of messages sent between agents minimize time required to store all load.

Sub-goals include evaluating how the different CRL policies exploit the higher load capacity at two servers in topology, and how well load is equalized among agents in the system. The topology in this experiment is a Grid; there are 48 agents with a capacity of 20 units, and 2 server agents with a capacity of units. The servers are placed at positions 47 and 48 in the grid, with the starting position at 0.

Load units are sent into the system via the agent at position 0. We compare the two different CRL policies CRL-discrete and CRL-gradient with both a random policy that selects a random action , and a dynamic programming DP solution that performs a breadth-first balancing of the load from the entry point. The CRL policies use a Boltzmann action selection strategy with a temperature parameter used to control the ratio of explorative to exploitative actions Sutton and Barto, The results for the CRL and random policies were averaged over 5 experimental runs.

The configuration parameters for the CRL policies are given in Table 1 , below. As illustrated in Fig. The dynamic programming DP policy is near optimal with respect to the number of time steps i. The CRL-discrete policy is also near optimal, as it is an exploitative policy that favors storing load over delegating load until an agent has reached its maximum capacity.

This effect can be seen in Fig. In Figures 7 - 10 , we can see how long the different policies take to discover and exploit the servers. The CRL and DP policies are more exploitative and tend to fill agents capacities sequentially from agent 0, leading to suboptimal load equalization, but they still compare favorably with the Random policy.

The measure we used to determine load equalization is the standard deviation of agent loads from the mean agent load in terms of percentage of capacity used at agents. Resource utilization is eventually maximized by all policies, while message passing is near-optimally minimized in both DP and CRL-Discrete. This exploitative policy favors storage actions at agents that are not fully loaded. Notice how agents are filled almost sequentially from the source of the load, agent 0.

This policy favors storage actions on servers, but becomes random when agents are almost fully loaded. Notice how quickly the server agents are almost discovered and exploited, even though they are 3 hops from agent 0. Grid Topology: Dynamic Programming policy.

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The goal of this experiment is, again, to maximize resource usage, and minimize message overhead, but this time in a random graph topology. In this topology, there are 48 agents with a capacity of 20 units, and 2 server agents with a capacity of units. Each agent has 10 different neighbors, randomly distributed from the set of available agents, but where an agent cannot be a neighbor to itself.

The servers are placed at positions more than 1-hop away from the starting position at 0. Load units are sent sequentially into the system via the agent at position 0. The same random topology was used to evaluate all policies, and the results were averaged over 5 experimental runs. Again, we compare the two different CRL policies CRL-discrete and CRL-gradient with a random policy that randomly selects an action from the local store action and the set of delegation actions , but the DP policy was not included as it does not finish, due to the presence of cycles in the topology.

The CRL configuration parameters were the same as in experiment 1, with the exception of the Temperature, which was set to 0. At the same time step, we added a discovery action to the 1-hop neighbors from agent 0 to enable them to discover the server located at a 2-hop distance from the source agent 0. As can be seen, the CRL-discrete policy quickly discovers and exploits the new server, while the CRL-gradient policy takes a longer time to do so.

There was also quite high variation in how long the CRL-gradient policy took to discover the new server, indicating a high level of randomness in its exploration. The upward spike near the end of CRL-gradient policy was a point where collaborative feedback that is, advertisements from the new server eventually influenced reached the origin agent 0.

The experiments show how CRL can be used to build a system that adapts to a dynamic environment. Agents interact with their local environment by storing loads and receiving feedback on available local storage capacity.

## Reinforcement Learning Papers Accepted to NeurIPS 12222

Through delegating load and locally storing load, agents collaboratively provide a load balancing service that is robust, adaptive, and can learn about and exploit new agents introduced into the system. The experiments could easily be extended to improve performance by adding asynchronous advertisements and adding heuristics, for example, adding memory to the DOP of the list of agents already visited prevent DOPs entering network loops. CRL, itself, is an approximate approach to online, decentralized reinforcement learning. It has similarities with population-based techniques such as ACO, particle swarm intelligence Kennedy and Eberhart, and evolutionary computing: the system takes a diverse set of DOPs as input, and it reinforces the selection of agents that were successful at solving the DOPs given the state of the system environment; this process improves system utility for a stable environment and can also adapt a system to better match its changing environment.

Rather than having agents die and be replaced by fitter agents, CRL agents decay their solutions to purge the system of stale information and use collaborative feedback to cooperatively learn new solutions. Distributed reinforcement learning is an emerging field that offers the promise of enabling the construction of distributed systems that can adapt and optimize their operation online. Existing approaches to distributed reinforcement learning include multi-agent control of a single MDP that describes system behavior, and decentralized approaches where agents are independent learners that collaborate to provide system services and collectively learn from one another to build local policies that improve system utility.

Designers of distributed reinforcement learning algorithms should give careful consideration to real-world properties of distributed systems, such as the high cost of message passing, and the possibility of failure for both agents and network connections. As a proof of concept, in this chapter, we showed how collaborative reinforcement learning can be used to build a load balancing system that can adapt to a dynamic environment. In the future, we anticipate that distributed reinforcement learning algorithms will be increasingly applied in a variety of domains, from large-scale grid computing systems, to optimize resource usage, to small-scale wireless and sensor networks, where power usage and radio transmission usage should be minimized.

In both cases, the goal of distributed reinforcement learning will be to replace existing parametric models with online learning models that can demonstrate improved adaptation to dynamic environments. The authors would like to thank Jan Sacha for an implementation of CRL in Java on which the experiments in this paper are based. Licensee IntechOpen. Help us write another book on this subject and reach those readers. Login to your personal dashboard for more detailed statistics on your publications.

Edited by Cornelius Weber. Edited by Olympia Roeva.

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Downloaded: Introduction Distributed reinforcement learning is concerned with what action an agent should take, given its current state and the state of other agents, so as to minimize a system cost function or maximize a global objective function. Challenges of Physical Aspects of Distributed Systems Physical aspects of distributed systems should be accounted for in any distributed reinforcement learning algorithm. These include: degree of centralization : centralization of system state or cost reward signals introduces both a bottleneck and a single point of failure in a system.

Distributed Reinforcement Learning Problem Definition Goldman and Zilberstein characterize multi-agent reinforcement learning as a decentralized control problem for stochastic systems Goldman and Zilberstein, Related Work on Distributed Reinforcement Learning In distributed reinforcement learning, actions by individual agents can potentially influence any other agent in the system.

Independent Learners An alternative to selecting joint actions is to allow agents take individual actions, with the goal that the collective behavior of the agents will minimize the system cost function Kok and Vlassis, Distributed Value Functions Schneider et al. Ant Colony Optimization The distributed control problem is also addressed by Ant-Colony Optimization ACO , a non-reinforcement learning based approach, best described as a meta-heuristic for producing approximate solutions to combinatorial optimization problems Dorigo and Stuetzle, Collaborative Reinforcement Learning The rest of this chapter concerns our work on collaborative reinforcement learning CRL , Dowling et al, ; Dowling, Cached V-values for connected states are decayed using the following equation: V s E CRL Learning Algorithm The CRL learning algorithm is a distributed model-based reinforcement learning algorithm with a cost model for network connections.

Our distributed model-based reinforcement learning algorithm for delegation actions is V j s ' E The system optimization problem is defined as minimizing the total cost of solving all DOPs where K is the number of agents in the system and Mi is the number of DOPs to be solved at agent i.

Experiment 1: Grid Topology: Balancing of Load over 48 Homogenous Agents and 2 Server Agents The goal of this experiment is to evaluate whether agents can exploit their total load capacity maximize resource usage , and minimize the amount of messages sent between agents minimize time required to store all load. Table 1. Experiment 2: Random Topology: Balancing of Load over 48 Homogenous Agents and 2 Server Agents The goal of this experiment is, again, to maximize resource usage, and minimize message overhead, but this time in a random graph topology.

Future of Distributed Reinforcement Learning Distributed reinforcement learning is an emerging field that offers the promise of enabling the construction of distributed systems that can adapt and optimize their operation online.

## Sample Efficient Multiagent Learning in the Presence of Markovian Agents - saclanislatu.ga

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Concentration of risk measures: A Wasserstein distance approach Sanjay P. IIT Madras. Elisa Celis Yale University. Can you trust your model's uncertainty? When to use parametric models in reinforcement learning?

### Doran Chakraborty

Chichilnisky Stanford University. Maddison Institute for Advanced Study, Princeton.

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## Decentralized Reinforcement Learning for the Online Optimization of Distributed Systems

Stock photo. Brand new: lowest price The lowest-priced brand-new, unused, unopened, undamaged item in its original packaging where packaging is applicable. The goal of this book is to develop MAL algorithms for such a setting that achieve a new set of objectives which have not been previously achieved. In particular this book deals with learning in the presence of a new class of agent behavior that has not been studied or modeled before in a MAL context: Markovian agent behavior.