Figure 1 : Meta-Reinforcement Learning as a transport problem and MetODS synaptic adaptation : a) Associating any task {\color[rgb]{0.0600000000000001,0.46,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.0600000000000001,0.46,1}\pgfsys@color@cmyk@stroke{0.94}{0.54}{0}{0}\pgfsys@color@cmyk@fill{0.94}{0.54}{0}{0}\bm{\tau}} in {\color[rgb]{0,0.5,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0.5,1}\pgfsys@color@cmyk@stroke{1}{0.50}{0}{0}\pgfsys@color@cmyk@fill{1}{0.50}{0}{0}\bm{\mathbb{T}}} to its optimal policy {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\pi_{\tau}^{*}}} in {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\Pi}} can be regarded as finding an optimal transport plan from {\color[rgb]{0.0600000000000001,0.46,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.0600000000000001,0.46,1}\pgfsys@color@cmyk@stroke{0.94}{0.54}{0}{0}\pgfsys@color@cmyk@fill{0.94}{0.54}{0}{0}\bm{\mu_{\mathbb{T}}}} to {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\mu_{\pi^{*}}}} with respect to the cost -\bm{\mathcal{R}} . Finding this transport plan is generally an intractable problem. b) Meta-RL approximates a solution by defining a stochastic flow in the policy space {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\Pi}} conditioned by the current task \bm{\tau} and driving a prior distribution {\color[rgb]{0.55,0.14,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.55,0.14,1}\pgfsys@color@cmyk@stroke{0.45}{0.86}{0}{0}\pgfsys@color@cmyk@fill{0.45}{0.86}{0}{0}\bm{\mu_{\pi_{0}}}} of policies {\color[rgb]{0.55,0.14,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.55,0.14,1}\pgfsys@color@cmyk@stroke{0.45}{0.86}{0}{0}\pgfsys@color@cmyk@fill{0.45}{0.86}{0}{0}\bm{\pi}_{0}} towards a distribution {\color[rgb]{0,1,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,1,0}\pgfsys@color@cmyk@stroke{1}{0}{1}{0}\pgfsys@color@cmyk@fill{1}{0}{1}{0}\mu^{\bm{\theta},\tau,t}_{\pi}} of policies with high score \bm{\mathcal{R}} . c) Density and mean trajectories of our model dynamic weights principal components over several episodes of the Harlow task (see section 5.1 ) reveal this policy specialization. Two modes colored with respect to whether the agent initial guess was good or bad emerge, corresponding to two different policies to solve the task.; Meta-Reinforcement Learning as a transport problem and MetODS synaptic adaptation : a) Associating any task {\color[rgb]{0.0600000000000001,0.46,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.0600000000000001,0.46,1}\pgfsys@color@cmyk@stroke{0.94}{0.54}{0}{0}\pgfsys@color@cmyk@fill{0.94}{0.54}{0}{0}\bm{\tau}} in {\color[rgb]{0,0.5,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0.5,1}\pgfsys@color@cmyk@stroke{1}{0.50}{0}{0}\pgfsys@color@cmyk@fill{1}{0.50}{0}{0}\bm{\mathbb{T}}} to its optimal policy {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\pi_{\tau}^{*}}} in {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\Pi}} can be regarded as finding an optimal transport plan from {\color[rgb]{0.0600000000000001,0.46,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.0600000000000001,0.46,1}\pgfsys@color@cmyk@stroke{0.94}{0.54}{0}{0}\pgfsys@color@cmyk@fill{0.94}{0.54}{0}{0}\bm{\mu_{\mathbb{T}}}} to {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\mu_{\pi^{*}}}} with respect to the cost -\bm{\mathcal{R}} . Finding this transport plan is generally an intractable problem. b) Meta-RL approximates a solution by defining a stochastic flow in the policy space {\color[rgb]{0.72,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0.72,0,0}\pgfsys@color@cmyk@stroke{0}{0.89}{0.94}{0.28}\pgfsys@color@cmyk@fill{0}{0.89}{0.94}{0.28}\bm{\Pi}} conditioned by the current task \bm{\tau} and driving a prior distribution {\color[rgb]{0.55,0.14,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.55,0.14,1}\pgfsys@color@cmyk@stroke{0.45}{0.86}{0}{0}\pgfsys@color@cmyk@fill{0.45}{0.86}{0}{0}\bm{\mu_{\pi_{0}}}} of policies {\color[rgb]{0.55,0.14,1}\definecolor[named]{pgfstrokecolor}{rgb}{0.55,0.14,1}\pgfsys@color@cmyk@stroke{0.45}{0.86}{0}{0}\pgfsys@color@cmyk@fill{0.45}{0.86}{0}{0}\bm{\pi}_{0}} towards a distribution {\color[rgb]{0,1,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,1,0}\pgfsys@color@cmyk@stroke{1}{0}{1}{0}\pgfsys@color@cmyk@fill{1}{0}{1}{0}\mu^{\bm{\theta},\tau,t}_{\pi}} of policies with high score \bm{\mathcal{R}} . c) Density and mean trajectories of our model dynamic weights principal components over several episodes of the Harlow task (see section 5.1 ) reveal this policy specialization. Two modes colored with respect to whether the agent initial guess was good or bad emerge, corresponding to two different policies to solve the task.