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This work focuses on online reinforcement learning (RL) in the presence of en- vironmental constraints. Specifically, we consider applications involving robot agents exploring in an environment where obstacles and unsafe zones are present, and the agents must maximize cumulative rewards and at the same time meet the environmental constraints. To address this challenge, we formulate the prob- lem using the constrained Markov Decision Process (CMDP) and incorporate the environmental constraint costs into the policy updates in the proposed Aug- mented Proximal Policy Optimization (APPO) algorithm. At each state and for each possible action, we apply a Variational Auto-Encoder (VAE) [1] to obtain a probabilistic estimate of the discounted cumulative future environmental con- straint costs and integrate them as a regularization term to the reward function. This augmented reward function updates the action-value functions within the APPO algorithm, which is trained by an efficient optimization scheme. Ex- perimental results demonstrate that our methodology enables robot agents to navigate within the safety-constrained regions effectively. 

The present work is a novel, systematic study of the effect of density functional theory input parameters on the vacancy formation energy (VFE), migration barrier for diffusion, and electronic structure for each element in the CoCrNi medium-entropy alloy (MEA). In particular, the novelties include: (1) calculating the aforementioned properties of Co, Cr, or Ni, in the CoCrNi MEA using magnetic and non-magnetic states, and two versions of the generalized gradient approximation: Perdew, Burke, and Ernzerhof (PBE) and the PBE version for solids (PBEsol), and (2) a detailed comparison of 0 K activation energy to experimental creep activation energies. First-principles calculations at 0 K are performed using the Vienna ab-initio simulation package. Special quasirandom structures (SQS) and Widom-type substitution are employed. For each element, Co, Cr, or Ni, non-magnetic calculations result in a higher VFE and larger range of calculated values for the configurations studied. The averaged migration barrier is the highest for Co in the CoCrNi for three of four sets of calculation parameters in the configurations studied. Finally, the results indicate that the average 0 K activation energy for diffusion makes up 70–80% of the experimental creep activation energy, depending on the exchange-correlation functional employed.